The United States and 10 other rich nations agreed yesterday to put up a $3 billion standby credit to protect Great Britain against sudden new [WORD ILLEGIBLE] of sterling balances held by other governments.

Following closely on the extension of a $3.9 billion loan to Britain by the International Monetary Fund, the new credit was greeted with relief by officials there.

Their concern had been that the shoring-up of the weak British financial structure by the IMF loan could be negated by the continual threat of the sterling "overhang," estimated at $3.8 billion at the end of September.

The dumping of sterling by both governments and private individuals was a key factor in the slump of sterling from more than $2 at the beginning of 1976 to as low as $1.60 a few months ago.

Yesterday's agreement, developed at a meeting of central bank officials in Basel, Switzerland, has two parts. THe first provides a $3 billion standby credit to the Bank of England, which can tap it to meet liquidation of sterling balances by official holders, that is, governments.

William Ryrie, British executive director of the IMF, noted in a telephone interview that "this will protect our reserves against outflows that may have nothing to do with balance of payments problems."

The second part will lead to a gradual reduction in the use of sterling as a reserve currency by other countries. To accomplish this, the British government will offer bonds, denominated in foreign currencies, to official holders of sterling. As the holders trade in the sterling for the bonds, the historic role of the pound as a reserve currency will be eliminated.

Edwin H. Yeo III, U.S. under secretary of the Treasury, who with Federal Reserve Chairman Arthur F. Burns helped to negotiate U.S. participation in the deal, said:

"This means that the sterling balances won't be a problem in the immediate future. Moreover, it represents a fundamental solution, because the British will be funding the balances" through the bond exchange.

According to a statement by the Bank for International Settlements in Basel, the bank will provide the standby line of credit to the Bank of England, backed by a $1 billion participation from the United States, and various amounts from Japan, West Germany, Belgium, Canada, Sweden, The Netherlands and Switzerland. Roughly the same group advanced a little more than $3 billion to the IMF so it could make the $3.9 billion loan earlier this month.

Part of the sterling balances problem has been psycholocal, stemming from persistent market worry about the "overhanging," as well as the direct liquidation of the balances themselves.

In the past two years, much of the sterling balances problem originated in sales by Arab nations, who once preferred to hold monetary recources in pounds. In mid-1975, Arab nations held about 75 per cent of total official balances, or a peak at that time of perhaps $6 billion worth. That total has been sharply reduced.

The arrangement yesterday did not deal with sterling held by private individuals, which may be another $4 to $5 billion. Although it is possible for some of that unofficial "overhang" to be converted into government balances, experts appear to believe that if the pressure of the official holdings can be neutralized, the basic problem will have been solved.