They call them "chop shops," places where stolen cars are expertly dismantled and the parts resold in a lucrative underground industry.

For the "mules" that steal the cars, it is a sophisticated business of supply and demand, where lists of the most prized car parts are matched against lists of where Mercedes and Sevilles and Lincoln Continentals are most easily found.

Now the federal government is wrestling with the problem. As part of a package of legislation designed to stem car thefts, Congress ordered the National Highway Traf- fic Safety Administration to deter- mine how car parts can best be marked to prevent their theft and reuse.

The NHTSA, however, faces some formidable obstacles. While everyone agrees that it's a good idea to try to stem the theft of auto parts, domestic auto makers, foreign manufacturers, insurance firms and law enforcement authorities disagree on the best way to go about it.

Which cars make up the so-called "high theft lines" that are the target of the bill? Which parts should be marked? Should the identification numbers be stamped onto the parts while the car is on the assembly line, or should labels be attached later? Should foreign car makers be forced to mark parts before cars are imported, or can it be done after the cars arrive here?

"It's a thorny and complicated issue that NHTSA has to deal with," said Stephen Weglian, a Justice Department attorney who is involved with the issue. "There are a lot of arguments."

The answers to those questions will determine how much the identification program will end up costing the auto makers and -- eventually -- consumers. The answers also will determine the effectiveness of the new law, which was weakened through compromises on Capitol Hill and still faces some resistance from the automobile industry.

The NHTSA's dilemma is heightened by the fact that no one knows the scope of the problem. In the words of Ford Motor Co. official Jerry Williams, trying to determine how many cars are stolen simply for their parts "is like asking how many people died of heart attacks when the Titanic went down."

About a million cars are stolen each year, according to Justice Department and insurance industry figures. The Chicago-based National Auto Theft Bureau estimates that of the half that are never re- covered, about 40 percent are dis- mantled for their parts. Car thefts are estimated to cost motorists and taxpayers about $5 billion a year, including the cost of higher insurance premiums and law enforcement.

The car parts legislation is just one part of the Motor Vehicle Theft Law Enforcement Act of 1984, which is aimed at making a dent in the booming stolen car industry. As part of the law, Congress also approved stiff new federal penalties for falsifying registration certificates; prohibitions against tampering with vehicle registration numbers; and tough new standards to control the import and export of cars.

"Since 1919 when Congress passed the Dyer Act, never in one month's time has so much criminal legislation been passed relating to stolen motor vehicles," Weglian said. "With all these provisions all enacted in October, the fed- eral arsenal has really been stocked up."

The law requires that major parts of frequently stolen passenger cars be inscribed or affixed with a permanent identification number, and that the process cost no more than $15 per vehicle.

In 1983, when the legislation was being drafted, members decided that about 60 of the 120 U.S. passenger car lines were "high theft lines" to which the law should be directed.

But when General Motors Corp. discovered that it produced 21 of the 60 most frequently stolen cars, the auto maker protested. Eventually, in a compromise with the company, Congress decided that no single auto maker should have more than 14 cars in the program.

"It's a very arbitrary figure," said Weglian. "It certainly wasn't desired by law enforcement. It kind of destroys the basic thrust of the legislation."

The requirement that parts be marked has the support of the auto insurance industry. "We've felt all along that the legislation will provide law enforcement with some of the tools that they will need to help control this crime," said Tim Kett, spokesman for the National Auto Theft Bureau, a 70-year-old organization supported by 500 insurance firms. "Once the parts are separated from the vehicle, there's little chance that they police can identify them."

But the automobile industry is lukewarm about the idea. It cites the lack of hard data on the problem, and contends that professional thieves are unlikely to be deterred by numbers attached to car parts.

"We may be spending a lot of money for nothing," said Bernard (Jerry) Riley, GM's vehicle security coordinator. He said that after a test marking program on GM's luxury Cadillac Eldorados and Sevilles in 1980 and 1981, "we did not see that marking those parts in and of itself had any impact at all."

"There's got to be a greater emphasis on law enforcement and in the courts to provide adequate punishment for these guys," Riley said. He added that insurance companies should be more diligent when they authorize customers to buy used parts to repair their cars.

At Ford, Jerry Williams, the senior staff engineer for state, local and consumer safety regulations, said, "For it to have any possibility of having an impact, the whole criminal justice system in respect to vehicle theft has to work. Now the vehicle thief doesn't get any real penalties. If the thieves get the message that the system doesn't work, then I don't think numbering our parts is going to have any impact."

Williams said that Ford had begun marking parts on some Lincoln Continentals, and that those cars had shown a declining theft rate. But Ford cars that had not been marked also showed a declining theft rate over the same period.

Charles Lockwood, vice president and general counsel of the Automobile Importers of America, seemed to sum up the sentiment of many in the automobile indus- try: "We did not support the legisla- tion for a variety of reasons," he said. "We will save our final assessment until we see the regulations."

The NHTSA has held a public hearing on the program, and expects to propose its regulations by January.