In recent months, the Federal Reserve has been severely criticized--in congressional hearings, lawsuits and elsewhere--for its new aggressiveness in trying to lure the check-processing business away from commercial banks.

Its chief critics are the very banks, most of them large, that have worked side-by-side with the Fed for more than 70 years processing paper and electronic payments, making sure that funds are transferred from the account of the check writer (the payor) to the account of the recipient (the payee)--a process that may route the check through as many as a half-dozen institutions.

The business of collecting checks deposited in other banks, savings and loan associations and credit unions is the key element of what is called correspondent banking.

The correspondent banks contend that the Federal Reserve is engaging in predatory pricing and other unfair practices in an attempt to increase its role in the check-processing business.

These banks argue that the combination of the Fed's regulatory powers, its nationwide presence and its ability to subsidize the costs of its check-clearing services (to the tune of more than $300 million last year) give the central bank an unfair advantage in its attempts to enlarge its role in what the General Accounting Office has estimated is a $24 billion business.

Because of the rising costs in banking and efforts by banks to force customers to pay for services they receive, the resolution of the dispute ultimately will have an effect on fees paid by depositors.

About 40 billion checks are processed each year. A large number of those checks are cleared locally (collected by the bank in which they are deposited)--bypassing both correspondent banks and the Federal Reserve.

But the checks that are written on accounts in banks distant from the one in which they are deposited must be routed back to the payor's bank. Moving the check from the point of deposit to the ultimate point of collection is the essence of check clearing.

Despite the vehemence with which the big banks criticize the Fed, the central bank today is processing a smaller percentage of the total check volume than it was two years ago. It used to process about 40 percent of the nation's checks. Its share now is about 35 percent.

That's only because the big banks have sharply reduced the prices they charge for check-clearing services to keep them comparable to the Fed's, according to Lawrence Russell, senior vice president of First National Bank of Chicago and head of a bank lobbying group called the National Payments System Coalition.

Banks used to make a profit on their clearing business, Russell said. Now, he said, most are losing money and many may be forced to quit the business. Russell said in an interview that the Fed may end up "nationalizing the correspondent banking system."

While the commercial banks are upset, many of the institutions that buy correspondent services--smaller commercial banks, savings and loan associations and credit unions--appear to be happy. They like the lower prices. The also like the new-found speed with which the central bank processes checks and also say the central bank is willing to offer services private banks cannot or will not.

Minneapolis Federal Reserve Bank President E. Gerald Corrigan admits that the situation is unique with the agency that sets rules for the banks now in direct business competition with them. He conceded in congressional testimony that there have been a "few rough spots" over the last few years, but said the Fed is properly fulfilling its congressional mandate.

That mandate, and the source of the controversy, is contained in the Monetary Control Act of 1980. One part of the act required the Fed to offer to any deposit-taking institution that is willing to pay for them services (such as check clearing) that the Fed used to provide only to banks that chose to be members of the Federal Reserve system.

The Fed member banks paid for the check clearing indirectly. They were required to keep large deposits (called reserves) on account with the Federal Reserve and were paid no interest on those deposits.

Now nearly all depository institutions--banks, savings and loan associations and credit unions--are required to keep reserves on deposit with the Fed. And all deposit-taking institutions that want the Fed to process their checks must pay for it.

Before the new law, depository institutions that weren't members of the Fed system were almost forced to use correspondent banks to clear at least some of their checks.

A savings and loan association with a check drawn on the bank next door could present the check to that bank for payment. But if the check were drawn on a bank 1,000 miles away, the S&L would give the check to its correspondent bank and pay it to collect the check.

The correspondent bank, almost always a member of the Fed system, was likely to use the central bank to clear the check if it was written for a small amount. Since the Fed was notoriously slow in collecting checks, the large correspondent banks developed their own transportation and delivery system to get big checks to their destination faster.

Backing up both the Fed and the private check-collection system is a vast network of couriers, bookkeepers and airplanes.

Since February, the Fed has speeded up its collection process. Part of the speedup was designed to make it more competitive with correspondent banks. It also is trying to fulfill another congressional mandate: to eliminate "float"--the extra billions of dollars that are created when the Fed has given credit for a deposit to one bank but has not yet collected the funds from the other bank.

Congress wanted to insure that the central bank competed with private correspondent banks on fair terms. The act said the Fed had to charge enough to cover its costs as well as as add a special "private-sector adjustment factor" to cover costs such as taxes and dividends the Federal Reserve does not incur but private competitors do.

The correspondent bankers contend that despite the law, the Fed is subsidizing its check-clearing and said the private-sector adjustment factor the Fed adds is not high enough.

Figuring out how to allocate costs to particular services is difficult, everyone concedes. For example, how much of the cost of heating the Baltimore Federal Reserve branch should be attributed to the check-clearing process.

But the Fed's Corrigan told Congress in June that the central bank has been "careful and methodical" and that the accounting is under constant review by the Fed and an outside accounting firm the central bank has hired.

Corrigan admitted that revenues fell short of costs last year, but said the shortfall was due to the decline in processing volume after the Fed began to charge for the service in September 1981. Check processing requires expensive overhead (mainly equipment), so a drop in volume cuts revenues far faster than expenses, while a boost in volume raises revenues faster than expenses.

Corrigan said that in recent months, revenues and expenses have been more closely matched.

The General Accounting Office, the independent arm of Congress, agreed that the volume decline had a major impact. However, William J. Anderson, the director of the GAO's general government division, told Congress in June the agency is studying recent Fed moves--including a February decision to raise prices and improve services--to see whether the Fed is fulfilling its mandate without subsidizing the services. That study is due in September.

First Chicago's Russell said the Fed not only subsidizes its check-clearing operation directly, it also does so indirectly. It forces costs on banks--microfilming, encoding and repairing damaged checks, for example--that it will not do itself. The Fed does not pay the presentment fees banks charge other banks that seek to collect on checks after a certain hour--usually around 10 a.m. The Fed can pick up checks from any bank, wherever it is located, while private banks cannot because of federal and state laws governing deposit-taking.

Corrigan said that the Fed's supposed advantages are in large part myth. The correspondent banks have advantages, too. They can use check-collection as part of a larger package of services offered to smaller banks. The private banks can pick their customers.

Russell said the big correspondent banks only want fair competition from the Fed. If that is not attainable, he said, the correspondent banks will support a bill introduced by Sen. William Proxmire (D-Wis.), the ranking minority member of the Senate Banking Committee.

The Proxmire bill would force the Fed to spin off its service activities into a separate corporation that would face the same constraints that private banks face in providing correspondent banking services to other financial institutions.