Rumors about the health of most major U.S. banks have cascaded through financial markets in the months following the massive run on Continental Illinois National Bank last May.

So far, the rumors have bounced off their targets. Since the Continental run, no major bank has been unable to raise the funds it needs in the money markets -- and big banks borrow tens of billions of dollars every day.

But both regulators and bankers are concerned that one day an unfounded rumor might cause a bank some funding problems or, in the worst case, start another run.

They also are concerned not only by the frequency and persistence of the rumors, but also by recent incidents in which rumors changed from vague reports that one or another bank was in trouble to a specific and plausible report of a problem that had no basis in fact.

Morgan Guaranty Trust Co., the most heavily capitalized of the major multinational banks, accelerated the release of its third-quarter earnings several weeks ago to quash several rumors -- including one that the big bank would report major earnings problems because of losses incurred in foreign exchange trading.

The unfounded Morgan rumor had an aura of reality, regulators and bankers said, because the bank is one of the biggest buyers and sellers of currencies in the world.

Morgan spokesman John Morris said the rumors appeared to emanate from Chicago financial markets, but neither Morgan officials nor regulators could identify a specific source for the rumor.

There was an identifiable source, however, in an attempt two weeks ago to plant a rumor about Manufacturers Hanover Trust with several news organizations and, apparently, the New York Stock Exchange and the Commodity Futures Trading Commission, which regulates financial futures trading.

A caller, identifying himself as a journalist, reported that Manufacturers had defaulted on a bond issue in Europe that it had sold to raise money to lend to debt-laden Argentina. The bond issue did not exist.

The caller reached United Press International and identified himself as a Business Week reporter. In subsequent calls, including one to a Manufacturers Hanover public relations official, he identified himself as a colleague of the UPI financial reporter that he first contacted. None of the phone numbers he left for callbacks were legitimate -- two had never been issued by the New York Telephone Co.

Regulators and bankers said the apparent attempt to plant the Manufacturers rumor was clumsy and ill-informed -- banks would never sell bonds in Europe to fund a particular loan -- and the journalists saw through it immediately.

Like the Morgan rumor, however, it had a tone of specificity and plausibility that could have upset markets. Manufacturers is the largest U.S. lender to Argentina. The caller also knew who to contact at several news organizations and the name of a floor broker on the New York Stock Exchange.

The broker never contacted the caller and when a public relations official at the exchange called back, he reached a bogus number.

Peter Bakstansky, a vice president at the New York Federal Reserve Bank said the unusual aspect of the Morgan and Manufacturers rumors was not that they specified an institution but that "they were about very specific problems that had no basis in fact."

Most of the rumors, however, name a specific bank but are rather general about the nature of that bank's supposed problem. They are of the "handwringing variety," according to an official of a major U.S. bank.

Officials think most of them spring up during volatile periods when investors, money traders and others are seeking explanations for sharp movements in interest rates or stock prices.

But the rumors also can change the complexion of markets in a matter of minutes -- to the benefit of traders or investors who have taken certain positions. For example, if investors become jittery about bank certificates of deposit, they may shift their funds into government securities -- driving up the rates on bank offerings and down the rate on bills.

Those changes would quickly be reflected in the prices of financial futures. But regulators said they have been unable to detect any pattern of trading that would suggest someone or some group was planting rumors in order to reap trading gains.

In the past week, the rumor mill has been quiet. Bankers and regulators hope that if falling interest rates keep financial markets calm, the rumors may die.

But they also said they are concerned that at some point a rumor, no matter how unfounded, could trigger a crisis of confidence in a bank or banks. It was a false rumor -- a story that U.S. regulators were seeking a foreign merger partner for Continental Illinois -- that sparked the run on Continental's deposits and led to the virtual nationalization of what once was the nation's sixth-biggest bank.

Continental, wracked by two years of growing problem loans, was more vulnerable than other banks to rumors. And because of its reliance on foreign depositors, it was harder to calm jittery depositors one or more continents away.

Other major money center banks have been strong enough to weather the rumors. But as one federal bank regulator noted, there are enough general concerns about the health of the banking system that rumors of one or another bank's difficulties that would have been dismissed out of hand two years ago now give investors and traders pause.

For example, only days after regulators put the finishing touches on the Continental rescue last September, its crosstown rival First Chicago Corp. stunned markets by announcing it was taking an unexpected loan write-off of $279 million in the third quarter and would have a large loss.

Quickly, reports spread that other big banks had shares in the same loans as First Chicago and that the write-off scenario would be repeated at other banks.

It was not.

Developments on both the international and domestic front add just enough nutrients to the broth to permit the continued birth of rumors:

*Most major U.S. banks have a heavy exposure to Latin American debtor countries, including Argentina, which continues to fall farther and farther behind on its payments.

*Declines in oil prices and low commodity prices increase investor anxiety over the health of energy and farm loan portfolios at big and small banks.

*Years of volatile interest rates and stock prices and the de facto failure of Continental -- three years ago considered the best-run bank in the country -- make traders and investors generally skittish.

In an attempt to instill confidence in themselves -- and as part of a general move toward caution among once go-go bankers -- most of the major money center institutions sacrificed some earnings in the third quarter to build up loan-loss reserves. They have also been adding capital -- the last line of defense against losses -- at a fast pace for the last 18 months. Regulators, as well as growing caution, have prodded the bankers to increase capital.

The most recent unfounded rumor had First Chicago Corp. as its target.

Reports wafted through the money markets on Oct. 24 that First Chicago could not raise the funds it needed on its own and was borrowing heavily from the Federal Reserve.

First Chicago was able to borrow all the funds it needed, regulators and bank officials said.

The only bank borrowing heavily from the Fed that day was Continental Illinois -- because Continental has been unable to raise enough of its own deposits for the last five months.

In a way, bankers said, that's a perverse reaction from the markets. Continental is the only bank in the country whose health is guaranteed by the federal government -- as a result of the rumors that brought it down last May.