MOSCOW— Not long ago, MDM Bank, one of the hundreds of modest-sized banks that sprang up here after the collapse of communism, offered a service that allowed Russian companies to cut costs, at the government's expense. Instead of paying salaries to their employees -- and the associated pension contributions to the government -- they gave the employees interest payments on company deposits in the bank.

Though MDM has discontinued this service, it is an example of the Alice-in-Wonderland world of Russian banking, where such complex maneuvers have been the order of the day.

''A major business for Russian banks is to find ways to do transactions in an economically efficient way,'' said Richard Hainsworth, the Moscow representative for Thomson Financial BankWatch, a credit rating agency. ''And that means getting around taxes and getting around obstructions. That is the way you survive in the Russian environment.''

Such was the state of banking here when billions of dollars slipped out of Russia from 1996 to 1999 in an alleged tax-dodging and money-laundering scheme that has resulted in some criminal charges, including those against a former Bank of New York executive.

American prosecutors have not charged the Bank of New York with any crime. Nor have they charged any Russian bank. But, seeking to untangle the maze, the prosecutors have been looking at MDM and three other Russian banks mentioned in documents filed in the Bank of New York case.

Lucy Edwards, a former Bank of New York executive, and her husband, Peter Berlin, pleaded guilty in February in Federal District Court in Manhattan to a range of criminal charges, including money laundering. According to the criminal charges filed against the couple, MDM and Sobinbank were the principal owners of DKB, one of two conduit banks involved in an operation that moved some $7 billion through front-company accounts at the Bank of New York. MDM and Sobinbank, the charges say, also moved money through correspondent accounts at the Bank of New York. Both banks said they helped raise new capital in 1996 for the other conduit bank, Commercial Bank Flamingo.

DKB has lost its banking license, according to the Russian central bank's Web site. Flamingo was raided last fall, and Russian prosecutors have brought charges of ''illegal banking activity.'' Sobinbank was also raided, but says it has not been informed of any charges against it.

MDM and Sobinbank both say they have done nothing wrong. They argue that what they did do they did at the direction of clients, and that the web of interconnections in Russian banking have confused prosecutors about their role. Gleb A. Kostin, the 30-year-old deputy chairman of MDM, argues that the only problem is ''the cultural difference'' between America and Russia. American prosecutors, he said, ''don't know anything about Russian banking.''

Nonetheless, a look at the banks mentioned in the case provides a glimpse of the tangled Russian banking world.

As Mikhail Kasyanov, Russian first deputy prime minister, acknowledged this month at a briefing in Washington, while inviting foreign banks' help in reforming the sector, most Russian banking institutions ''have never been banks in the real sense.''

Often, they were the private preserves of their owners, known as ''pocket'' banks or political banks, giving the owners a ready source of money for investments. Banking and tax regulations, coupled with inconsistent oversight, encouraged banks to offer ways around high tax rates, onerous employment requirements, foreign exchange rules and regulations that made it hard for Russian companies to get their hands on even a small amount of cash. In addition to catering to their insiders, Russian banks moved a lot of their assets out of the country, setting up operations in favorite offshore banking havens.

''You had almost no chance of finding a Russian company absolutely clean, from a legal point of view, in the early and mid-1990's,'' said one Russian banker. ''The job is to separate those who did do something illegal but are still honest from those who are doing something illegal and are dishonest.''

Sobinbank's 1998 annual report, the latest one written under international accounting standards, suggests it was a pocket bank, existing for the needs of its investors. It gave out 80 percent of its loans to just five borrowers that year. Though it would not say who the five were, the report said that 58 percent of its loans that year were to the energy sector, 12 percent to space and aircraft and 4 percent to cities and municipalities. The bank's major investors, directly or indirectly, include Russia's largest natural gas company, a top oil producer, a major space company and the developer of a major underground shopping mall linked to the Mayor of Moscow.

The report also shows that Sobinbank moved a big portion of its assets -- nearly 40 percent -- outside the country. In 1998, Sobinbank had foreign exchange transactions totaling 3.14 billion Russian rubles (about $515 million before the August 1998 devaluation and about $110 million at current rates) with one related party that the bank refused to name. The transactions indicate it was outside of Russia.

MDM, whose formal name is Moscow World Business Bank, and Sobinbank are, typically, politically well connected. And they illustrate the intertwining relationships common in Russian banking.