It is the ultimate financial nightmare.

At the end of the business day, a major bank does not have the funds it needs to make good on the hundreds or thousands of payments it made that day to other major banks over one or another of the nation's electronic funds transfer networks.

Another bank, counting on receiving money from the defaulting bank, finds itself unable to meet its obligations. It then defaults and triggers a default at yet another institution. Defaults cascade. The U.S. banking system collapses.

Bankers and bank regulators agree that there is only a minuscule chance that a systemwide collapse would occur because of the failure of a bank to "settle" its accounts at the end of the day.

But the awesome consequences of that eventuality, however improbable, have moved the Federal Reserve Board and the banks themselves to begin to take steps to reduce the amount of risk they are exposed to from the hundreds of billions of dollars worth of electronic payments that whirl across computer networks each day.

Last month, the Federal Reserve Board told banks they should set two types of "voluntary" limits -- one to reduce the risk any individual bank poses to the system if it should fail to settle; the other to reduce the risks to itself if a bank should default on its payments.

The source of the problem is the phenomenon called the "daylight overdraft."

Because any individual bank may send out payments early in the day but not receive the payments it is due until later, at any given point during the day its accounts with the Federal Reserve or with one of the privately owned electronic transfer systems could be overdrawn.

If the bank failed to receive enough cash by day's end to make good on all the payments it transmitted, there could be a crisis in the banking system.

Collectively, overdrafts may reach $110 billion at their midday peaks before disappearing by the end of the day, the Fed said.

"There definitely is credit risk involved" when banks use the domestic electronic systems to transfer funds," according to Donald R. Hollis, senior vice president of the First National Bank of Chicago. He said the Fed's moves, along with similar steps by the banks themselves, will reduce that risk.

Robert J. O'Keefe, senior vice president of American Security Bank, said that use of electronic payment systems has grown "fantastically" in the last 10 years, sharply increasing the trauma to the domestic and international banking system in the event a major bank fails to settle up one night.

A Federal Reserve study several years ago constructed a "representative" large bank, based on the composite payments receipts and transmissions of several large banks. It found that the representative bank started and ended the day with a surplus of $1 billion in its account at the Federal Reserve -- where all interbank accounts eventually are settled. But at points in the day, it owed $3 billion more than it had received.

The potential problem is international in scope. Not only U.S. banks use domestic electronic transfer systems. Many foreign banks are major users, too, according to O'Keefe. The foreign banks use U.S. banks as agents to make and receive payments on their behalf.

The failure of a major foreign bank could trigger an immediate crisis in the U.S. payments system. In fact, the only time there was a problem in settlement -- one that was resolved -- occurred in the aftermath of the failure of the West German bank Herstatt in 1974.

There are four electronic payments systems in operation today: three are privately owned; the other is owned and operated by the Federal Reserve.

Fedwire is used by more than 2,000 banks to transmit payments on their own behalf or on behalf of bank and nonbank customers. The Clearing House Interbank Payments System (CHIPS) is run by the New York City Clearinghouse Association. CHIPS has 137 banks -- either U.S. banks or U.S. branches or agencies of foreign banks -- that can make and receive payments in their own name.

Only 21 of them are involved in the toting-up process at the end of the day, however. The other 116 members must clear their accounts using one of the 21 settling banks -- including the 11 New York City banks that are members of the clearing house. Non-CHIPS banks cannot pass or receive payments in their own name, but must do so through a correspondent bank.

Fedwire and CHIPS are the giants of the transfer systems (often called wire transfer by bankers).

Fedwire carries about 166,000 payments a day that have a total value of $366 billion, according to David B. Humphrey, assistant director of the Federal Reserve's division of research and statistics. Humphrey said CHIPS carries about 91,000 payments every day with a total value of $277 billion.

The dollar amount of wire transfers that crisscross CHIPS and Fedwire each week nearly equals the $3.9 trillion in goods and services that U.S. citizens produce each year.

There are two other wire transfer systems, but they pale by comparison to Fedwire and CHIPS. Cashwire and CHESS (which Chicago banks use to make payments among themselves) together carry fewer than 1,000 payments each day with an aggregate value of less than $1 billion.

The nightmare scenario of cascading defaults could occur only on a private system -- where banks zip payments to each other all day long but settle up with each other at the close of business.

The Federal Reserve guarantees a payment once it notifies the recipient bank that the funds have been transferred. If the sending bank fails to cover its daylight overdrafts on Fedwire by the end of the day, the central bank must absorb the loss.

But all payments on CHIPS are provisional. No actual funds are transferred from one bank's account at the Federal Reserve to another bank's Fed account until settlement time, normally about 5:45 p.m. There has never been a situation in which the 21 settling banks on CHIPS have failed to square their accounts. Every daylight overdraft has been covered -- usually by a combination of receipts from other banks and normal overnight borrowings from banks with excess funds. These overnight borrowings are called federal funds.

Experts say that the way the federal funds market works is in part responsible for the size of daylight overdrafts at many big banks. For the most part, big banks are net buyers of federal funds while smaller banks are net sellers.

Starting about 9 a.m., the buyers begin to return their overnight borrowings. At about 3 p.m., the funds begin to flow back to the buyers. It is during the period from 11 a.m. until 3 p.m. -- when federal funds are under control of the sellers -- that daylight overdrafts are at their peak.

The rest of the overdrafts occur because banks usually are unable to time perfectly their receipt of funds with their payments. As a result, a certain level of daylight overdraft is inevitable under the current system, bankers say. If banks had to wait for anticipated funds to appear before sending off payments, all wire transfers would be so bunched that the payments system would face the electronic equivalent of rush-hour gridlock.

For the most part, banks know what payments they are supposed to make and what payments they can expect to receive -- whether for their own account or for those of their customers.

As the day wears on, banks get a clearer and clearer picture of the funds they will receive and the funds they must send out. Adding that information to all other data it has about its inflows and outflows of funds -- plus the cushion it always keeps -- the bank knows roughly how much it will have to borrow that day, mostly in the federal funds market.

But a catastrophe could strike. Suppose it made payments on behalf of a foreign bank client over CHIPS -- which is used mainly for international payments -- and the foreign bank is declared insolvent and does not cover its payments. Or three major borrowers fail to make their interest payments as scheduled. The CHIPS bank might not be able to meet its obligations.

The bank can try to find sources of funds to replace missed payments. The Federal Reserve discount window is one source. The federal funds market is another -- although at 5:45 p.m. finding banks with funds to lend might be difficult. CHIPS can delay settlement time to permit a bank to scrounge up needed funds. The Fed can keep Fedwire open after 6 p.m. to permit those funds, if found, to be transferred to the cash-short bank.

But the Fed and banks believe the best way to avoid a settlement default is to limit the risks that daylight overdrafts provide to the system and individual banks.

To reduce the chances of a settlement default on the private networks or of a major loss to the Federal Reserve on Fedwire, the central bank has told banks that they should:

* Put a limit on the net amount they can be owed by any other bank. The Fed calls these bilateral net credit limits. By establishing a net credit limit, the bank would minimize the amount of loss if the other bank defaults. For example, if the credit limit is $200 million, and at 2 p.m. the bank has sent payments of $50 million and received payments from the other bank of $250 million, it would accept no more payments from that bank. If the other bank defaulted, the maximum loss would be $200 million because the bank would not make good the $50 million it transferred to the defaulting bank.

* Place a ceiling on their own daylight overdrafts. The Fed calls these limits sender net debit caps. A sender net debit cap reduces the total amount of loss to the banking system that would occur if a bank defaulted. The caps are set in relation to a bank's capital. Healthy banks can average daylight overdrafts that are equivalent to twice their capital. Weak banks would not be able to engage in a daylight overdraft.

The caps would have to be measured across all electronic payments systems. If a bank has a $2 billion cap on its overdrafts, it could be in overdraft by $1.5 billion on CHIPS and $1 billion on Fedwire. But then it could send no more payments over any system until it received payments that reduced its net overdraft position.

The Fed said that any private payments system that does not require its members to set both types of caps would not be eligible to use the Federal Reserve's facilities to settle accounts. Without being able to use the Fed system to transfer funds back and forth from one bank's Fed account to another, a private wire transfer system would find it impossible to function.

Even before the Fed put forward its "voluntary" rules last month, however, the private systems were moving to reduce daylight overdraft risk. CHIPS already has a bilateral credit limit and is working on imposing an overall cap. Some banks, to protect themselves, already imposed similar restraints on their own payments.

First Chicago's Hollis said he is worried that the Fed's proposal may go too far and too fast.

But a major New York bank official said that limits on daylight overdrafts are the best route to insuring the safety and soundness of the payments system.

He said that the banks that want to resist it are those that do not want to spend the money to improve the efficiency of their electronic transfer systems.