A criminal underworld of Soviet emigres, some of them skilled in white-collar crime and hardened by Soviet prison and labor camps, is reaching beyond its base in Brooklyn, using extortion and violence in its own neighborhoods and engaging in multimillion-dollar racketeering schemes on an international scale.

The network of Russian-speaking criminals is small and loosely grouped compared with the hierarchies of traditional American organized crime. But camouflaged within the country’s growing Soviet immigrant communities, the network is fast outstripping the ability of local and Federal agencies to curb its illegal schemes, some of which are linked to Mafia crime families, officials of the Federal Bureau of Investigation and other agencies say.

Intelligence reports trace the network to black marketeers and other professional gangsters, many of whom plied their criminal trade in the Soviet Union before winning exit visas – or being planted – in the wave of Jewish emigration.

One mob boss who was said to have spent 10 years in Soviet prisons before turning up in Brooklyn was known to enforce his threats with an electric cattle prod he kept in his car. Investigators say he once extorted $15,000 from another immigrant by threatening to kill the man’s daughter on her wedding day. Another crime kingpin, convicted of credit card fraud and now facing extradition from West Germany, is reputed to have amassed a fortune of more than $600 million from bootlegged gasoline in less than a decade after he arrived from Odessa.

As Soviet emigration policies loosen up, greater numbers of Jews, Armenians and ethnic Germans have been given permission to leave. Since 1975, some 150,000 have come to the United States. About 50,000 have settled in the New York area; another 15,000 are expected to settle here this year.

Law-enforcement officials say that, while the network comprises no more than a few hundred active criminals out of all those who arrived, some of these are highly skilled mob enforcers, forgers and confidence men.

Their criminal activities range from old-fashioned jewelry swindles on 47th Street to multimillion-dollar schemes involving fake credit cards and bootlegged gasoline. They have also counterfeited millions of dollars in currency and bank and corporate checks. In New York City, the Secret Service is planning to announce soon that it has smashed a Soviet emigre crime ring charged with counterfeiting $20 million and fleecing American Express of millions more in bogus travelers checks.

These criminals have also forged antiques, passing some off as products of Faberge, the famous jewelers of czarist Russia; engineered insurance frauds; trafficked in illegal drugs, and resorted to assault, torture and murder where they have found resistance.

Investigators say the crimes typically involve get-rich-quick schemes, often executed with a contempt for an American criminal justice system that seems benign compared to the brutalities of life in Soviet labor camps and prisons. Law-enforcement officials say that the transplanted criminals, reared in a system where goods are scarce and corruption is a cost of doing business, can exploit opportunities in the American system – taking advantage of the credit system and other commercial relationships based on trust. Hardened Criminals After Soviet Jails, Little Daunts Them

”They feel we are pussycats,” said one New York detective monitoring the network, ”and the United States is one big candy store.”

”The Russians just don’t care -they’re not afraid of the consequences,” said John Good, a retired F.B.I. agent who ran the Abscam case. He now works for a private security concern, Business Risks International, which has been hired by victims of some of the schemes.

Despite the obstacles, law-enforcement agencies have made some progress against the emigre underworld. Besides the Secret Service counterfeiting investigation, a grand jury in Brooklyn has been hearing evidence in an extensive anti-racketeering inquiry into Soviet immigrant criminals.

In one unpublicized case under F.B.I. investigation, a Soviet emigre crime ring infiltrated one of the nation’s largest jewelry manufacturers and methodically stole gold and gems valued at $54 million from the Manhattan company, Jardinay Inc. In another case, in March, the police in Frankfurt, West Germany, arrested Marat Balagula (pronounced bala-GOOL-a), a 45-year old Soviet emigre and suspected gasoline bootlegger who fled the United States in November 1986, while awaiting sentencing for a major charge-card fraud, and led Interpol on a five-continent chase. Execution-Style Murders

The police in Brooklyn also report a wave of violent crime in the Russian-speaking communities – including murders with all the characteristics of organized crime executions. One shootout with automatic weapons, which took place outside a Brooklyn gasoline wholesale company in 1986, leaving one dead, and two wounded, involved associates of Mr. Balagula – including three co-conspirators in the credit card scheme. In November 1987, Boris Rubinov, a 30-year-old immigrant, was shot to death in Brooklyn, two months after he was arrested while loading more than two dozen rifles and other guns into the back of a car.

The growing economic clout of the emigre crime network is particularly troublesome, said Laura Brevetti, a Federal prosecutor in Brooklyn who heads a joint strike force tracking far-flung gasoline tax evasion schemes. ”Money is power and the fact that they are making so much money illegally makes them powerful,” she said.

”The Russians add a zero to anything that anyone else thinks of,” said Michael Flanagan, the assistant special agent in charge of the criminal division of the F.B.I. in New York.

Some relocation officials, though, challenge the specter of a spreading Russian Mafia as painted by law-enforcement agencies.

”It is a quantum leap to jump to a statement that there is an organized Mafia,” said Mark Handelman, executive vice president of the New York Association for New Americans, a Government-supported Jewish resettlement agency in Manhattan. Since 1972, he said, the agency had been contacted by the law-enforcement authorities no more than three or four times about suspected criminals. Soviet Compliance I.N.S. Is Unable To Screen Felons

Although most of the new arrivals and many of the criminals are Jewish, investigators say, some of those who arrived as Jews in fact forged their identity papers in order to leave the Soviet Union. Also, investigators said, some are undoubtedly K.G.B. agents smuggled into the United States among legitimate immigrants. They also believe that the Soviet Union has deliberately rid its prisons of some troublemakers by sending them here.

Federal agents say the Immigration and Naturalization Service, in the absence of cooperation from the Soviet authorities, is in no position to weed out those with forged documents and criminal pasts among the thousands of immigrants passing through transit camps outside Rome.

The crime network has centered in the bustling Brighton Beach neighborhood with its Old World shops and restaurants, but police reports show that criminal offshoots have also surfaced in Los Angeles, San Francisco, Seattle, Phoenix, Chicago, Cleveland, Minneapolis, Milwaukee, Dallas, Miami, Wilmington, Baltimore, Philadelphia, Boston, and Providence. Canada has been investigating a Soviet emigre crime network in Toronto with links to Italian organized crime.

Groups are often organized by city of origin – Odessa, Kiev, Leningrad, Moscow – giving some structure to the otherwise loose-knit network that appears not to be based on turf. Police say the network is usually subordinate to the deal of the moment.

In many ways, the Soviets follow the pattern of other ethnic organized-crime groups in America, preying first on their own and then, when they feel strong enough to evade the law, spreading out. said James Fox, director of the F.B.I.’s New York office. Educated, Technically Skilled

But, unlike other immigrant criminal groups, the Soviets generally arrive well-educated and highly skilled technically, said Lydia Rosner, a Russian-speaking assistant professor of sociology at New York City’s John Jay College of Criminal Justice who wrote a 1986 book, ”The Soviet Way of Crime.”

”They are often more skilled than Americans themselves at exploiting the weaknesses in American society,” she said. For example, she said, the official Soviet passion for identity documents has long nurtured a forgery underground that enables criminals, once here, to assume many identities, thwarting police efforts to keep track of them. Some also use false documents to collect welfare benefits and build up credit ratings.

”To them,” Mrs. Rosner said, ”our police are Mickey Mouse.”

Although United States law bars the deportation of immigrants who can show they face persecution in their native country, the Immigration and Naturalization Service says that since 1980 it has returned 101 emigres with criminal records to the Soviet Union. Early Swindles Bags of Gold Rubles Turn Into Potatoes

A recent report circulated among law-enforcement agencies dates criminal activities back 15 years to Brighton Beach’s ”Potato Bag Gang,” a group of confidence artists from Odessa who, posing as merchant seamen, picked out other immigrant ”marks” and offered to sell them antique gold rubles cheap. A sample coin was authentic, but when the victims paid thousands of dollars for sackfuls of them, the bags turned out to be full of potatoes.

In a similar swindle involving a supposedly antique necklace, a Long Island hardware store owner, who took pity on a couple posing as newly arrived immigrants, was bilked of his life savings of $70,000.

Considerable information on the network’s leaders was provided by an anonymous informant who in 1983 sent Kenneth P. Walton, then a deputy F.B.I. director in New York, a manuscript in Russian entitled ”All About Russian Mafia.” Much of the information was subsequently corroborated. Bosses Develop Extortionist Toting A Cattle Prod

At the time, the informant said, the head of the network was Evsei Agron, a 51-year-old Leningrad-born immigrant, killer, extortionist and thief. With his bodyguards, his cattle prod and the aura of his Soviet prison time, Mr. Agron was a fearsome figure as he made his rounds of Brooklyn, with a weekly visit to the Russian baths in the East Village.

In January 1984, Mr. Agron was shot in the neck outside his apartment house at 100 Ocean Parkway in Park Slope. He survived, telling a Russian-speaking detective he would ”take care” of the attacker himself. During his recuperation, doctors removed old bullets from previous shootings. Three sources told the police that the shooting was linked to a disputed drug deal.

In May 1985, Mr. Agron was shot to death as he came out of his apartment en route to the baths. His bodyguard and driver, Boris Nayfeld, who had been waiting downstairs, left mysteriously after the shooting. Conflicting Explanations

Informants later told the police that Mr. Agron had been killed for seeking a cut of criminal profits while withdrawing from active leadership. But other reports said he had been murdered by the Mafia for poaching on its activities.

Mr. Agron was listed as vice president of a Brooklyn fitness club that had been the scene of a drug murder in 1982 and that also had distant links to members of Italian organized crime, including John (Sonny) Franzese, then listed as the underboss of the Colombo family. Mr. Franzese also joined forces with Soviet emigres in concocting a highly profitable gasoline tax evasion scheme exposed by Ms. Brevetti’s task force. One of the conspirators, Michael Markowitz, who assisted the authorities, was shot to death in his Rolls-Royce in Brooklyn in March.

No sooner was Mr. Agron out of the picture than his bodyguard, Boris Nayfeld, turned up in the employ of Mr. Balagula, who investigators believe succeeded to Mr. Agron’s authority.

Born in Odessa on Sept. 8, 1943, Mr. Balagula worked in the Soviet Union as a storekeeper on passenger ships in the Black Sea, according to sources within the emigre community. He came to the United States on Jan. 13, 1977, with his parents and became a citizen in 1984.

Informants cited in intelligence reports say he may have connections to Soviet intelligence, but Mr. Balagula, in an unusual sworn statement to the Federal Bureau of Investigation, flatly denied any contacts with Soviet secret services. He said he emigrated ”because of anti-Semitism” and in order to raise his children ”in a free society.”

Intelligence files say Mr. Balagula was an owner of one or more restaurants in Brighton Beach. When he fled the country in 1986, Mr. Balagula had been convicted, along with several other Soviet immigrants – including Boris Nayfeld and his brother, Benjamin – in a scheme that fabricated charge cards with names and real account numbers of Merrill Lynch customers. The cards were used to run up fictitious sales with the complicity of several merchants. No goods changed hands, but Merrill Lynch ended up liable for up to $300,000 in losses. Balagula ‘The Power Broker’

Wiretaps showed Mr. Balagula to be ”the power broker at the center,”said Assistant United States Attorney John P. Pucci of the Eastern District of Pennsylvania.

During the trial in Philadelphia, the bald, paunchy Mr. Balagula rented a suite at the Hershey Hotel and came to court every day in a stretch limousine.

”You hear all kinds of stories about Mr. Balagula,” said Ms. Brevetti. One has Mr. Balagula purchasing an island off South Africa, or land in Senegal. Another has him masterminding a fleet of supertankers docking all around the world. Before his arrest in West Germany, he was sighted in Atlantic City and California, Paraguay, South Africa and Hong Kong.

Hans-Hermann Eckert, a court spokesman in Frankfurt, West Germany, where extradition proceedings were nearly complete, said rumors had circulated of a large bribe about to be paid to free Mr. Balagula. Targets Get Bigger Jewelry Industry Proves Vulnerable

The Soviet emigre network’s criminal schemes have also focused on the jewelry industry, court records and investigators say. One of the largest thefts victimized the workshops and offices of Jardinay, a manufacturer of watches and gold jewelry at 155 Avenue of the Americas at Spring Street.

Founded as a small watch-making company some 20 years ago by a Hungarian family, the company has grown into a $100 million-a-year business with its own designer line called Helen Z, which is sold to Bloomingdale’s, Saks, Fortunoff, J. C. Penney, and other retailing giants.

By 1986, investigators said, some 25 emigres had infiltrated the 300 employees and brazenly diverted or stolen nearly $54 million in gold and diamonds before the scheme was discovered in an inventory the next year. Only $2 million worth was ever recovered.

”The place was filled with Russians,” said one astounded investigator. ”They were taking out finished product and raw materials and stocking their own jewelry stores in Staten Island, Long Island and California.”

The jewelry business – where merchants traditionally entrust each other with millions of dollars in gold and gems on a handshake – is particularly vulnerable to fraud. In some cases, emigre swindlers have set up phony jewelry exchanges, where they ostentatiously lock their customers’ valuables in a safe. Once the customer leaves, the safe is emptied through a hidden door at the back. Sophisticated Forgeries Bogus Cash, Faberge Eggs

In addition to jewelry, the criminal schemes also include counterfeiting of currency and bank and corporate checks, Federal agents say.

In its investigation of what it calls a $20 million counterfeiting ring, the Secret Service is preparing to announce the arrests of up to 20 suspects, said Richard Ward, the special agent in charge in New York. Almost all of the money has been recovered, along with many bogus bank checks and nearly $4.5 million in counterfeit American Express checks that had been cashed around the world, he said.

The emigre network’s members also fabricated bank checks of Manufacturer’s Hanover Trust and Citibank.

Art forgery is also prevalent, investigators and jewelers say. Delicately bejeweled eggs, made by emigre craftsmen in workshops in Astoria, Queens, have been passed off as original Faberges and sold to a major auction house, investigators say.

In May 1987, Itsik Ben-Eli, an emigre who was being sought for questioning in a homicide in Brighton Beach the month before, was arrested at Kennedy airport with a woman who had 700 grams of heroin – about 1 1/2 pounds -taped to her body. Mr. Ben-Eli’s fingerprints were later found on the tape. He was also carrying two freshly minted counterfeit $100 bills. At his sentencing in Federal court in Brooklyn, a man claiming to represent an Israeli organization urged the court to let Mr. Ben-Eli serve his sentence in Israel. The judge sentenced him to five years in Federal prison. Growing Violence Desperate Victim Shoots Loan Shark

Much of the violent crime inside Soviet emigre communities can be traced to protection and loan sharking rackets seen among other immigrant groups. Often, it is only when these transactions turn violent that they become known to the authorities. People familiar with the Russian-speaking community say transplanted ”People’s Courts” exist, where men of influence settle disputes, some of them brought over from the old country.

One emigre, Valery Zlotnikov, was repeatedly hounded over a debt by another emigre, Felix Furman, a convicted killer who had managed not only to escape prison in Colorado but also to jump bail on a gun charge in New York. Mr. Furman furthermore was acquitted of attempted extortion, even though an exchange of money took place under the eyes of the police. Last December, in despair, Mr. Zlotnikov shot Mr. Furman dead on the street in Brighton Beach and turned himself in.

In another convoluted case, a grocer named Vyacheslav Lyubarsky was strung up from a ceiling light in his store when he failed to repay $40,000 he lost in a card game. He later shot one of his tormentors and, with two reputed Mafia members, went on to stage a faked jewelry robbery in Chicago, in an abortive attempt to collect a $750,000 insurance claim. ”They even beat up a woman to add credibility,” said Detective Peter Grinenko, a Russian-speaking investigator assigned to Brooklyn District Attorney’s squad.

American law-enforcement officials acknowledge they are ill-equipped to deal with the cultural and language complexities of the Soviet emigre crime problem. While the F.B.I. has a task force that often deals with these crimes, their Russian-speaking agents are generally reserved for counterintelligence work. In New York City, the Police Department’s leading intelligence analyst for Soviet emigre crime, Joel Campanella, retired this month, and associates are ncncerned that his expertise has been lost.

Two years ago, the police intelligence section lost another expert, a Russian-speaking police officer who could answer a police hot line number circulated in Brighton Beach for tips on criminal activity. One day recently, when a distraught Russian-speaking woman called twice, offering information, there was no one at the police desk who could understand her.