Three years after the start of the current economic recovery, the nation's banks remain riddled with problem loans.

Bank customers -- both corporate and consumer -- are adding to their debt burdens at rates many analysts consider to be excessive, leaving them and their creditors vulnerable to either a sharp increase in interest rates or a severe economic downturn, according to economist Henry Kaufman, executive director of Salomon Brothers Inc., the big Wall Street investment banking firm.

"We really won't know what the situation is until we get to the next recession," Federal Reserve Board Governor J. Charles Partee said.

Because the economy continued to grow in 1985 and because interest rates continued to fall, the banking system as a whole avoided any brushes with disaster like the near-failure of Chicago's big Continental Illinois National Bank in 1984.

On the whole, analysts said, the system got stronger.

The shaky loans didn't get any better, but the banks' abilities to absorb loan losses did, according to James McDermott, vice president of Keefe, Bruyette and Woods, the New York securities firm that specializes in banks and bank stocks.

Few important borrowers sunk into financial difficulties because of the growing economy. Declining interest rates made it easier for borrowers to pay their bankers and enabled most banks to earn more from their loans. In general, banks do better in periods of declining interest rates because they reduce the rates they charge borrowers more slowly than their own costs of funds decline.

Banks, on a far more conservative track than they were five years ago, took many of the profits they earned from their loans and added them to the reserves they maintain against loan losses. Higher reserves increase a bank's ability to absorb losses from problem loans that deteriorate into bad loans.

But the overall improvement in the banking system -- and record profits in the beleaguered savings and loan industry -- mask some severe "pockets of vulnerability," according to McDermott.

A large number of banks did not share in the general improvement -- including some large ones, like San Francisco's Bank of America. The nation's second-biggest bank is riddled with loan losses that eat up the revenue the bank is piling up on the loans that are being paid on time.

Most of the problems are concentrated among banks that were heavy lenders to industries that did not get better during the three-year old economic recovery: agriculture, energy and shipping.

The biggest banks also have a large number of outstanding loans in Latin America, where nearly all countries have borrowed too much and are finding it difficult to repay on time. The major debtor nations -- Brazil, Mexico, Argentina and Venezuela -- are paying on time today.

But many of these big money center banks, rather than reporting higher profits to shareholders, are using a high proportion of their interest payments from Latin American loans to bolster their reserves against the day when a major borrower might repudiate its debt.

In recent months, a glut of office space in a number of major cities has driven down rents and boosted vacancies, making it difficult or impossible for a number of developers to repay construction loans.

Concerned by reports of real estate difficulties, the Office of the Comptroller of the Currency, which regulates federally chartered banks, recently completed a survey of 60 big bank real estate lenders.

Although the comptroller's office uncovered a number of problem loans at those banks, the agency's chief national bank examiner, John Downey, said the real estate situation is not as weak as the agency anticipated.

Last year a post-Depression record 120 banks failed -- although most of them were small and their demise posed little threat to either the banking system as a whole or the federal fund that insures deposits in all but a handful of the nation's 15,000 banks.

L. William Seidman, the new chairman of the Federal Deposit Insurance Corp., predicts that a similar number of banks will fail in 1986. The agency -- which insures deposits up to $100,000 and takes over the "estate" of banks that fail -- has determined that 1,141 banks are sufficiently weak that they are on the list of problem instititions that get special attention from the FDIC.

Some of the banks on the list are on the brink of failure. Others will be if they don't right themselves soon. Most problem banks, if history is a guide, take the proper steps to bring themselves back to health.

A large number of savings and loan associations, the traditional lenders to home buyers, are in desparate shape, despite the record $5 billion the industry as a whole earned last year. A recent General Accounting Office study estimated that 465 of the nation's 3,100 S&Ls are broke, but permitted to continue in business by federally created accounting gimmicks.

Many of the sickest savings and loans are those that sought to recoup the losses they encountered in the late 1970s and early 1980s by making high-yielding, but risky loans in which S&Ls have little expertise.

Savings and loans lost money in the 1970s and early 1980s because the income they earned from their portfolio of fixed-rate mortgages was far less than they had to pay for deposits. The S&Ls that survived the lean years and stuck close to their traditional activities are recovering today.

On the other hand, a large number of today's problem commercial banks are those that stuck with their traditional lending: the agricultural banks.

Once uncommonly healthy, farm banks today account for a disproportionate number of the nation's problem banks. Five years of declining agricultural prices have taken their toll on farmers and farm lenders alike. Analysts do not expect the farm economy to improve in 1986 and predict that farm bank failures will continue at a heavy clip.

The decline in oil and other energy prices has hit hard at banks in the Southwest, particularly in Oklahoma and Texas. The nation's worst banking crisis in 50 years -- 1984's near failure of Chicago's giant Continental Illinois National Bank -- had its roots in Continental's excessive lending to Oklahoma oil and gas drilling firms that went bankrupt during the decline in energy prices that began in 1981.

In Texas, banks were hit hard by the steep decline in oil prices and the growing glut of office space in major centers.

Last fall, bank regulators issued new guidelines that require institutions to be more rigorous in putting shaky real estate loans on their lists of problem assets. Putting a loan on its list of problem assets generally reduces the earnings a bank can count from the loan and often goads the bank into further reducing earnings by putting a portion or all of the interest payments it receives into loss reserves.

The key problem areas in the U.S. financial system -- agriculture, energy, real estate -- are unlikely to show much improvement this year.

But Stanley Silverberg, director of research at the Federal Deposit Insurance Corp., said that the generally rosier economic forecasts for 1986 suggest that banks that are not heavy lenders to the weakest sectors of the economy should improve their lot.

Which is a good thing, according to Salomon Brothers' Kaufman. "While the whole financial system showed a little progress in 1985, it is the kind of system that cannot tolerate a recession soon nor tolerate soon a significant return to a tighter monetary policy" that would drive up interest rates, he said.

Not only have corporations and businesses borrowed heavily, in many cases business have replaced equity (stock) with debt -- through mergers that have been financed with bank borrowings or bonds and through leveraged buyouts in which purchasers buy the company by borrowing against the assets it will acquire. In many cases, companies have bought back their own stock, depleting their cash reserves to do so.

Every dollar of debt that a business substitutes for a dollar of equity increases the organization's vulnerability. If the economy faces the type of double-whammy that hit in the early 1980s -- when interest rates surged to record levels at the same time a severe recession was in progress -- bankruptcies and bank problems would mushroom.

Kaufman warns that the nation is entering its fourth year of economic growth. All recoveries peter out, he said, and the longer one continues, the more likely it is to end sooner rather than later.

But he cautioned that the U.S. financial system -- buffeted by problem loans and overextended borrowers -- cannot afford a downturn soon.

"Not this year," he said. "Not next year. And next year is not that far away."