The nation's Farm Credit System is facing potential losses of $11 billion -- the largest loss ever incurred by any related group of U.S. financial institutions.

Lobbying on Capitol Hill last week for a federal bailout, representatives of the 37 farm credit banks said they need $10 billion in federal help to save the $74 billion system from bankruptcy.

Privately, they told senators that FCS now estimates it has $11 billion worth of bad loans, congressional sources said. Even though that would be the largest such loss in U.S. history, some analysts think the number could turn out to be higher.

Worried Reagan administration officials fear that the $10 billion plea is only the first of what will be a substantial number of cries for costly help from financial institutions that are in trouble as a result of declining inflation.

Along with the farm banks, the savings and loan industry is seeking government aid, and there are proposals to provide relief for banks with large loans in Latin America that are not likely to be paid on time, officials say.

The total cost of bailing out the S&Ls and the Third World lenders could be several times what FCS is seeking, they say.

In most of the cases, the problems are a direct result of falling values of farm land, real estate and other assets acquired by borrowers who expected inflation to keep roaring along. Now some of the borrowers -- and their lenders -- are in trouble.

The issue is who is going to have to swallow the losses generated by this process of disinflation -- the borrowers, the lenders or the nation's taxpayers?

The administration, already faced with enormous federal budget deficits, is in no mood to be generous with the taxpayers' money.

This unhappy choice of who loses and in what proportion was highlighted last week when Edwin J. Gray, chairman of the Federal Home Loan Bank Board, told the House Banking Committee that many bankrupt thrift institutions are being kept open solely because the Federal Savings and Loan Insurance Corp. doesn't have enough money to pay off depositors if the thrifts were closed.

Even after raising $759 million by boosting deposit insurance premiums, the insurance fund has only $3.2 billion in usable reserves, Gray said, adding, "The fund must be recapitalized."

There are three possible sources of the needed money, Gray continued, the U.S. Treasury, the thrift industry itself or, if FSLIC were merged with the healthy Federal Deposit Insurance Corp., the nation's commercial banks. The FDIC insures deposits at commercial banks, which despite the greatest number of failures since the Depression, are in vastly better shape as an industry than the thrifts.

"I personally favor recapitalization by the industry as I strongly suspect you do also," Gray told the committee. He said that what is needed is about $8 billion that could come from assessing each thrift institution 1 percent of its deposits. Skeptical committee members later got him to acknowledge that another 50 to 100 shaky thrifts would be forced out of business if they had to make such a payment.

The thrift industry, of course, doesn't want to pay, as spokesmen for one of its major trade groups quickly made clear.

Still in the background is a potential federal involvment in a variety of proposals to alleviate the continuing Latin American debt crisis. Treasury Secretary James A. Baker III wants major U.S. banks whose loans there are already in trouble to lend $20 billion more to Latin American nations. This would allow nations such as Mexico and Brazil, who together already owe nearly $200 billion, to buy more time to improve the competitiveness of their economies.

Lending a troubled borrower more money is a time-honored technique to prevent having to record a loss on a loan. The Farm Credit System, the Federal Home Loan Bank Board and many commercial banks lending to farmers have used this approach. In fact, bank regulators and state and federal government officials earlier this year urged lenders to use forebearance in dealing with debt-ridden farmers.

Though not as well-developed as the bailout plans for the thrifts and farm credit system, proposals keep surfacing to help the debtor nations and their bankers. The plans call for creating some sort of agency or bank to "warehouse" some of the bad loans, and in the process write off some of the debt on which the countries have to keep paying interest.

However, moving an asset -- a loan is an asset to a lender and a liability to a borrower -- off the balance sheet of a bank or any other business normally means that any loss must be recognized for accounting purposes. If part of a loan is forgiven, the bank ordinarily must show that amount on its books as a loss, which would weaken its financial standing. The banks might be able to avoid taking the losses if the federal government were to buy the bad loans for their full value.

Some analysts, such as Harvard University Prof. Jeffrey Sachs -- who is overseeing a research project on foreign debt for the National Bureau of Economic Research -- believe that the Baker approach of trying to buy more time will not succeed because there is little prospect that the countries in question will be able to service their existing debt, much less the additions Baker is urging.

Instead, Sachs said, the creditors should agree to write down the debt to, say, 75 percent of its face value if the nations make the internal changes needed to improve their economies. The write-down would reduce future debt service costs and could be held out as an incentive to make the changes.

Again, the question is one of who is to absorb the loss. Some administration officials fear that, if they ever agree to the first bailout, a long line of claimants will form outside the Treasury door. If they do it in a case such as the Farm Credit System, where there is no current federal liability, "then where can we draw the line?" asked one official on a Cabinet Council on Economic Policy task force that has looked into the farm credit and thrift problems.

The Farm Credit System, or FCS, would use the $10 billion it is seeking -- in the form of a long-term, non-interest-bearing loan from the Treasury -- to finance its own warehouse of bad loans, which would be gathered up from the several hundred units within the system.

FCS consists of 37 banks -- a federal land bank, a federal intermediate credit bank and a bank for cooperatives in each of 12 regions of the country, plus an interregional bank for cooperatives. In addition, there are several hundred local production credit associations, which obtain funding from the intermediate credit banks and lend annual crop financing to farmers. There are also local land bank associations that make long-term loans to finance machinery and farm land purchases, with funds provided by the land banks.

Despite the word "federal" in names such as "Federal Land Bank," the FCS long has stressed that all of the federal seed money that helped it get started and expand was repaid some years ago.

Today, FCS is in such deep trouble that its representatives say it cannot survive for long without at least the $10 billion worth of federal assistance. According to a recent General Accounting Office report, if the system were to follow the rules that apply to commercial banks, it could rack up $7.6 billion worth of losses by next June.

The FCS books are in such bad shape, and accounting practices so varied among its hundreds of units, that no one knows with confidence just how bad the situation has become. The administration asked Congress to postpone hearings on the assistance proposal that had been scheduled for last week until better data are available. Administration officials say they are not buying that estimate of $11 billion worth of bad loans without better evidence.

Whatever the actual loss turns out to be, it seems clear that it will dwarf previous losses by a related group of institutions in the United States. All the past profits the FCS has managed to salt away over the years very likely will be wiped out by the middle of next year and its farmer-owned capital will be in jeopardy.

Commercial bankers in farm areas have complicated the debate over the FCS by arguing that, if the land banks and production credit associations get a bailout, they should, too. After all, commercial bankers point out, private lenders provide about 60 percent of the seasonal credit used by farmers to finance planting and harvesting of their crops. If some farm lenders are to get help, shouldn't all of them?

None of the farm credit bailout proposals has found favor with the administration. "I haven't heard any very good argument that says we have a liability there, and I don't think we can afford to take on any that we don't have to," one Reagan official said. Treasury Secretary Baker has told system representatives that there is no federal money available now.

A recent study of the nearly 1,200 ag banks in the Kansas City Federal Reserve District by Robert Craig West, an economist for the bank, concluded that most of the institutions were so well capitalized after several years of very strong earnings in the late 1970s and early 1980s that few are likely to fail."Under the most likely assumption about loan quality, West said. over 90 percent of all ag banks have capital above the minimum 5 percent guideline, at least in the short run," West said. "Of the remainder, only 1 or 2 percent should be viewed as potential failures in 1985. However, the continued erosion of net income suggested by the simulations will further weaken ag banks . . . . "

In some parts of the country, such as Oklahoma, bankers are more interested in getting some relief from bad loans they have made to the oil and gas industry than from those made to farmers, says according to Mark Drabenstott, research officer for the Kansas City Fed Bank.

"The bottom line of all this is that there are a lot of losses to be borne out there," Drabenstott said. "The issue is, who is going to bear them? We have gotten to a crossroads, and the government may be involved. There is not a clear-cut economic answer. It will have to be a political answer."

Building a political consensus to bail out the Farm Credit System and the savings and loan industry, to say nothing of all the other claimants who the administration fears might line up, will be very difficult in a time of great pressure to hold down federal spending.