For years, the Soviet Union has been known as a fast payer, a Communist nation so anxious to maintain its slim links to the capitalist trading system that its checks were in the mail as soon as the bills arrived.

Now, however, the bills are piling up on the desks of Western businesses.

The change came about six months ago, and Western business groups and economists estimate that the Soviet Union is now about $10 billion behind on its payments to foreign suppliers, many of whom are complaining that the level of Soviet debt is beginning to pinch their cash flow.

Stanislav V. Assekritov, deputy chairman of the USSR Council of Ministers State Commission for Economic Reform, said here last week that the delays are only temporary, caused by bureaucratic snafus as the Soviet Union moves from a centrally controlled trading system to one in which as many as 1,500 state enterprises can buy foreign products on their own.

But some international bankers are concerned that the slow payments may be a symptom of a fundamental cash flow problem. One economist said the Soviets began running short of money after spending so much of their hard currency over the winter, buying scarce food and consumer goods to satisfy striking miners and other citizens dissatisfied with empty store shelves.

As a result, U.S. grain traders have been asked to wait two to three months for payments; Du Pont Co. said it is owed $16 million for agricultural chemicals by the Soviets but believes it is a temporary problem; and, according to reports from Tokyo, four major Japanese steel companies -- Nippon Steel, Kawasaki Steel, Sumitomo Metal Industries and NKK -- are holding up shipments after Soviet debt to them mounted to $100 million.

"The Soviets have a credit problem ahead, but they are still creditworthy," said John P. Hardt, the Soviet specialist at the Library of Congress's Legislative Research Service.