Administration officials are quietly studying options for dealing with problems in the financially troubled Farm Credit System, the farmer-owned cooperative banking network that holds more than a third of U.S. agricultural debt.

The system of 37 banks, formed after World War I, is regulated by a quasi-federal agency but is financed independently through the sale of farm credit bonds.

However, the specter of specific federal guarantees or some form of direct aid has been raised by growing problems of bad loans and fleeing borrowers.

The administration's public position is that Farm Credit must use its own resources to cope with its problems, but there is mounting opinion at the Agriculture Department and on Capitol Hill that some sort of federal aid may be required to keep the system whole.

A general weakening of the FCS' ability to market bonds or failure of any of its lending components could injure the system's overall health and put new pressure on commercial banks and the federal Farmers Home Administration, the other key elements in agricultural financing, to provide credit to farmers. Additional shocks could be felt by banks, which regularly buy FCS bonds.

These and other concerns about the slumping farm economy, stemming from low income, falling exports, high interest rates and sinking land values, have led the administration to form a Cabinet-level task force. Both President Reagan and Vice President Bush have been briefed on the situation in recent weeks.

"We feel very strongly that the FCS has the resources to deal with its problems and that it should do so. We want to give them the chance. But if they haven't acted by Sept. 1, it could get away from them in some areas," one high official said.

Agriculture Secretary John R. Block, however, has gone further in recent public statements.

He said in Iowa two weeks ago that the administration is considering ways to help the FCS, adding that he "seriously" doubts that the system can remedy its woes without federal help.

"Most everyone thinks the Farm Credit System is federally supported, and the federal government is obliged to save the day, and certainly there is no question about it that a system with $80 billion in loans is not going to be allowed to go down the tubes," Block told a convention of corn growers.

Block alluded again this week to the possibility of federal assistance, even though the FCS has more than $6 billion of untapped reserves, but he warned that federal help would be contingent on the system's accepting more regulatory oversight -- anathema to the professionals who run the system.

Agriculture Undersecretary Frank W. Naylor Jr., who oversees credit-related issues at the department, would say only that the administration is "monitoring developments in the FCS very closely. We must insist that the system use its own resources to deal with this . . . . [But] in the end, the system is too critical not to remain as the major component in agricultural lending."

Concern also is mounting among farm-state legislators, who have expressed increasing worry about the system. Just before recessing this month, the Senate unanimously adopted a resolution urging the FCS to work out its problems but reasserting a government responsibility to help keep it healthy.

Rep. Cooper Evans (R-Iowa), who has raised questions about FCS procedures and proposed a number of legislative remedies, said this week: "The question is not whether we have to do something. The question is what and when. I think that by the end of September the administration and the FCS will come hand in hand to Congress for some help."

The FCS's 37 borrower-owned banks are scattered across a dozen districts around the country. Operating funds are raised through the sale of bonds, then lent to farmers through locally based federal land banks (for farm purchases) and production credit associations (for short-term operating money). The Farm Credit Administration, based in McLean, Va., regulates the system.

The system accounts for roughly $80 billion of the $215 billion agricultural debt in this country. The rest of farm credit is provided by commercial banks, the Farmers Home Administration and other institutional and private lenders.

Overall, despite record loan losses in the last four years, FCS balance sheets depict a strong and generally profitable lending entity with adequate reserves to deal with pockets of weakness in the most economically troubled farming regions. Less than 13 percent of all FCS loans are described as "nonperforming" -- delinquent or in worse shape.

But a major problem, because of the FCS' decentralization and local control, lies in its inability to move its reserves quickly to trouble spots. A reorganization that would streamline the system and permit shifting of assets from healthier districts to ailing districts is being pushed by system officials.

Six years ago the FCS, in a move to get lower interest rates for borrowers, agreed to interlocking arrangements that provided for loss-sharing among the scattered districts. But a flaw in that arrangement, some analysts say, is that loss-sharing is not triggered until there is an actual default in one of the member institutions -- too large to allow for preventive actions by the system.

System officials from Farm Credit Administration Governor Donald E. Wilkinson on down, in efforts to maintain bond-market confidence in the FCS, have insisted repeatedly in recent weeks that the network is sound and fully capable of handling its current difficulties.

Wilkinson earlier this month said the FCS would not need federal help as long as the farm economy deteriorates no further. "There is no question that FCS does have some credit problems," he said. "But it does not have a problem with capital adequacy. At this time, it does not require an infusion of capital, from the government or anywhere else."

The system's problems drew national attention last year when FCS members were required to go to the rescue of the Spokane, Wash., district, which faced collapse when millions of dollars of loans went bad. Closures and mergers of other troubled production credit associations, plus a flood of borrower complaints about managers' abusive tactics, have kept the spotlight on the system.

The current focus is on the Omaha district, which provides financing for 19,000 farmers and ranchers in the economically hard-hit Grain Belt of Iowa, Nebraska, South Dakota and Wyoming, where a combination of low prices and tumbling land values has created intense stress.

The Federal Intermediate Credit Bank of Omaha has approximately $1.6 billion in loans spread among 37 production credit associations in the four states. But as of March 31, $587 million of that was in the "nonperforming" category. Officials acknowledge that the situation has worsened since then.

As a result, Omaha district loan interest rates have gone as high as 16 percent to help cover the losses. That in turn has prompted an exodus of many of the more secure borrowers from the system, leaving the district with a weakened portfolio. Other districts will vote this month on a proposed transfer of $340 million of FCS reserves to prop up Omaha.

"The very measures they are taking are a disaster for many farmers," Rep. Evans said. "FCS officials have focused on saving the system rather than on helping individual farmers. Higher interest rates and restrictions on the withdrawal of capital are breaking the backs of many borrowers . . . . Faith in the system is very important. It will take a generation to repair the damage and loss of faith by farmers in their lending institution."

The system's moves to consolidate offices and services and the proposals to shift funds from the more prosperous districts to the needy areas have set off a wave of member resentment and turned usually friendly congressmen into severe critics.

And the defensive reaction of some FCS officials has deepened the emotions.

Rep. James Ross Lightfoot (R-Iowa), for example, said he was outraged when his complaints about management practices drew a brusque reaction from the head of the Omaha district.

"Please don't debate with the Omaha district on this issue," district president John A. Harling wrote. "It is simply destroying us to have you saying that our business decisions are faulty."

Lightfoot, however, is only one of many critics. A protest movement that began in Texas, one of the more prosperous FCS areas, has gone nationwide with the formation of the National Association of Farm Credit System Stockholders.

The group's leader, Luman W. Holman, a rancher from Jacksonville, Tex., charges that FCS officials have exaggerated the system's credit problems as a step toward removing farmer controls at the local level.

"If the financial figures are accurate, there is no reason to paint a dark picture," Holman said. "Either they have lied or distorted the figures, or they have an ulterior motive of gaining control. The system was organized for the benefit of farmers and ranchers. Our problem is that our employes have taken over the system."