The new Soviet leadership under Yuri Andropov is mounting a law-and-order campaign on a scale not seen here since the days of Stalin.

The government's lightning attack on absenteeism and alcoholism during the past few weeks, according to older Moscow residents, could be compared to similar but far more brutal drives carried out during the late dictator's rule.

Apparently trying to make it clear that he means business, Andropov has unleashed posses of deputized vigilantes into the streets. The raiders have visited virtually every major public establishment, from movie theaters and restaurants to hairdressers' and public baths to search for those who had improperly taken time off from work.

A reported raid on the Sandunovsky Bath, a favorite haunt here, was the talk of Moscow. According to various reports, the vigilantes and police sealed off the bath at midday and found hundreds of persons, including some high-ranking bureaucrats, who were unable to provide a convincing explanation for absence from their desks.

The vigilantes are Communist Party members deputized for limited duties and assured of police support. People caught have not been arrested but their names were taken for forwarding to their superiors.

The other aspect of the current campaign is the struggle against corruption and illegal profiteering.

Senior police officials announced two weeks ago that they have developed a new informational system to allow them to carry out "preventive" activities in "practically every apartment building" in the city. The system provides the police "not only with the basic demographic data" about inhabitants of these buildings but also with "evidence" about people engaged in violations of "the socialist norms of social life."

For the first time, the Soviet media have begun to question the source of wealth of some members of the elite. Pravda recently carried several articles about high party officials misappropriating state funds to build country homes for themselves and to purchase automobiles and various luxury items. Another Moscow newspaper charged that party officials were using their membership in the Communist Party as a "permit" for personal enrichment.

Andropov appears to be using the law-and-order issue to gain time while new economic measures are being prepared for the next plenum of the party Central Committee. The drive seems directed at two crucial problems.

One is the long-entrenched looseness of labor discipline, which seems to grow out of the nature of the Soviet economy and is a major factor in shortages, poor-quality goods, delays in services and overall inefficiency.

The other is corruption and illegal private dealings that form the basis of a thriving underground economy. As Soviet society grew more affluent in the 1970s, the underground economy became a key lubricant for the rigidities of the centrally planned system, providing access to virtually all goods and services for those who have either money or important connections.

The two activities are linked to the extent that they have produced a complex network of payoffs throughout the society. A Moscow taxi driver writing in the weekly Literaturnaya Gazeta recently described a payoff system he was involved in. According to his account, he regularly has to bribe police, mechanics, the taxi dispatchers and various inspectors just to hold his job.

What economic tools the government is preparing to deal with the situation is not clear yet. However, while the vigilante raids are apparently a temporary measure to shock the nation out of its lethargy, the law-and-order drive is expected to continue and to be used by Andropov in his struggle against the bureaucracy.

The measures undertaken so far seem to enjoy popular support. Since abstenteeism has become a risky business, long food lines have become noticeably shorter, barber shops are not crowded at mid-morning, and it has even become pleasant to take a ride on a Moscow city bus.

Authorities, meanwhile, have improved the supply of food to the shops. This week it was possible to buy, without waiting in line, items ranging from Egyptian tangerines to meaty frozen chicken from Western Europe. The drive has also sharply cut the number of persons who previously traveled from provincial towns to Moscow to shop.

Judging by the press comments and letters to the editor, the authorities appear to be generating support for their actions at the grass roots.

If there is opposition to the measures, it is only visible among shop managers and sales personnel. The manager of a hairdresser's recently was complaining that her shop was empty one morning when it would have been full a few months ago. "I won't be able to fulfill the plan," she said. The plan, upon which the salaries of personnel are based, was made on the assumption that the practice of leaving one's job for two or three hours to have one's hair done would not be suddenly broken.

In a dairy shop recently, the clerk left her post for a few minutes and when she returned she found a line of angry women. One of the customers reminded the woman that Andropov has been urging everyone to work efficiently and that she should not simply leave her job.

"Andropov, Andropov," grumbled the clerk. "They all say it. I am sick and tired of Andropov."