Banking depends upon confidence. Without it, even the soundest of banks and banking systems would collapse.

That confidence has been strained recently by a worldwide recession that has triggered a wave of industrial bankruptcies and near bankruptcies and caused severe economic problems in many important developing countries where private banks have lent hundreds of billions of dollars.

The chance of major failures among the 15,000 big and small banks that lend in international markets, while not expected, is still real enough to trouble financiers and regulators. The risk is "more than zero," according to one senior U.S. official.

The safety net beneath that network is the willingness of the industrial world's central banks -- such as the Federal Reserve, the Bank of England or the West German Bundesbank -- to avert a crisis by intervening as "lenders of last resort."

The central banks of the 11 industrialized nations have agreed to take responsibility for their national private banks, even when these are operating abroad.

The details of the agreement have never been made known despite its importance to the security of the international economy. The agreement was reached after a small German bank collapsed in 1974 -- in the midst of another crisis period for the international money system -- threatening to pull down others with it.

If a bank has a shortage of lendable funds -- a liquidity problem in central banker argot -- the lender of last resort pumps funds into that institution to permit continued operations and prevent a panic. More than once in potential banking crises here -- the most recent being the failure of Drysdale Government Securities last May -- the Federal Reserve has stressed publicly its role as lender of last resort.

That assurance alone usually calms depositors who fear they will not be able to obtain their funds from a troubled bank.

The goal of the agreement among the 11 central banks is to extend that assurance to the $2 trillion international banking market, where banks lend and borrow in currencies other than their national currency--where London banks might lend dollars or German banks lend pounds, and where no formal lender of last resort exists.

The agreement is called the Basel declaration after the home of the Bank for International Settlements in Switzerland where the central bankers of the industrialized countries meet regularly.

Describing their agreement, the governors of the central banks recognized that it would not be practical to lay down in advance detailed rules and procedures for the provision of temporary liquidity. But they were satisfied that means are available for that purpose and will be used "if and when necessary."

The details are deliberately kept vague. The central bankers of the 11 nations -- the United States, Japan, West Germany, Canada, Britain, France, Italy, Belgium, the Netherlands, Sweden and Switzerland -- do not want to "go around offering everybody a bailout," Federal Reserve Governor Henry Wallich said last week. That would be such an inducement to rash lending practices that it would create a "moral hazard," he added.

Broadly, however, the 11 nations have sorted out which of them is responsible for which bank in the huge and complicated international banking market, with the essential precept that a central bank is ultimately responsible for branches and subsidiaries of its own banks.

If an overseas branch of a U.S. bank needs emergency cash, for example, the "parent" is deemed responsible, and the Federal Reserve is thus the lender of last resort. With overseas subsidiaries, the line of responsibility is not quite as clear cut -- a subsidiary is not an integral part of a bank in the way that a branch is, but a separate company. However, "the principle of parenthood still prevails," Wallich said.

Suppose a subsidiary or overseas branch of a New York bank runs short of cash. The parent bank in New York is expected to supply whatever dollars are needed to bail out the branch or subsidiary. If this pushes the parent bank into trouble, then the Federal Reserve stands ready to lend it as much cash as it needs, although at premium interest rates. The same is true for banks with headquarters in other major countries: a New York branch of a Japanese bank in trouble is the responsibility of the Bank of Japan, a British bank should be bailed out by the Bank of England, and so on.

While the lender of last resort may be the parent country, central bankers have decided that regulation or supervision of banks is the responsibility of the host country.

In practice, things are rarely this simple. Central banks are worried most of all about their own markets. It is likely the Federal Reserve would be involved if a foreign bank with operations in New York or San Francisco crashed, or threatened to, and it is concerned as a regulator about the health of overseas branches and subsidiaries of U.S. banks.

Central bankers do not promise to stop any bank from failing -- in the sense of wiping out its capital and losing shareholder money. They are more concerned to protect depositors, and thus shore up the confidence that makes people trust their money to a bank. Some large depositors did lose money in the recent collapse of Penn Square, the small Oklahoma bank that failed July 5 -- although federal insurance took care of the smaller ones -- and that increased market jitters.

But while the Fed allowed Penn Square to fail, most of the world's bankers assumed that no central bank could permit a major multinational bank to fail, no matter what the circumstances. "Penn Square isn't Citibank," said one regulator.

Nevertheless, the Bank of Italy's recent unwillingness to stand behind a Luxemburg affiliate of failed Banco Ambrosiano has called into question the effectiveness of the safety net in the eyes of some financiers. The failure of the bank itself, however, was handled normally by Italian authorities.

U.S. regulators said that because the affiliate was only partly owned by the Italian bank, had non-Italian investors and its own Luxemburg charter, the responsibility of the Italian authorities was limited and properly exercised. Luxemburg, which has no lender-of-last-resort facilities, has written other banks with affiliates there telling them to take direct responsibility for them or close them down. Presumably if the Italian bank were directly responsible for the affiliate, the Bank of Italy would have acted differently.

In all bank regulation and support, distinctions blur. In the United States there is a firm line between insolvency and illiquidity--institutionalized with the Federal Reserve as lender of last resort and the Federal Deposit Insurance Corporation as the receiver in a failure. In practice, it often is hard to distinguish between the two and in many countries the central bank is responsible for dealing with both anyway.

One further complication that worries many financiers is that the Basel safety net, such as it is, does not directly cover all of the "at least 15,000 banks" that, according to one expert, are operating in the international markets. The 11 nations party to the bail-out agreement account for about 80 percent of international lending, a senior U.S. official said.

"What about an Arab bank in Singapore or Bahrain that gets into difficulties ?" a monetary official remarked rhetorically. The industrialized nations would have no direct responsibility. "What happens if banks in Argentina, for example, find it difficult to renew dollar deposits?" another banker queried, adding, "the central bank has no dollars to spare."

Whatever their formal responsibilities, in practice the industrial nations could not fail to step in. When Mexico ran short of cash, major nations mounted an immediate operation to provide the nation with enough dollars to stay afloat.

The banking system is such an integral part of the economy that a central bank anywhere would likely bail out its own banks if necessary, financiers hope. If the central bank then needs international help to provide the needed cash, the bank bail-out merges into a general rescue package.

When a country faces a problem like Mexico's, its final step -- after emergency cash problems are solved -- is the International Monetary Fund.

The fund, in return for pumping money into the country, usually demands that the country take steps to put its financial house in order.

The IMF's resources, however, are limited -- particularly in comparison with the huge flows of private capital through the Euromarket. In addition, debtor nations are often unwilling to go to the IMF because of the austerity measures that are typically a condition of a fund loan.

Many central and private bankers believe the IMF's resources -- which are provided by governments -- should be increased sharply so that the multilateral agency is able -- and, perhaps just as important, thought to be able -- to supply emergency cash to nations that cannot meet their debt obligations and cannot raise enough new money on the commercial market.

Ever since the first oil crisis in the early 1970s bankers and international officials have worried about whether the world can manage the huge task of recycling cash from surplus to deficit nations. The private banking system has in fact done the job much more smoothly than most expected.

But as bankers begin to worry about the creditworthiness of developing nations and begin to pull in their horns, the future efficiency of "recycling" can be questioned.

"We have allowed a situation to develop where private banks are responsible for virtually all lending," one senior New York banker said. There is "no balance between bankers and official lenders . . . and no bounce" in the system, he warned.

He and many others -- including several U.S. officials -- believe that the IMF's resources should be increased rapidly as soon as possible so that it can play a bigger part in recycling.

Officially, the United States is against too large an increase in the fund's regular resources, based on the quotas, or currency deposits from member-nations. That is "a fundamental error of judgment," the New York banker said.