The nation's money supply continued its puzzling behavior last week as it slipped below September levels to $359.5 billion, the Federal Reserve reported yesterday.

Normally, the basic money supply known as M-1 -- the total of currency in circulation and checking accounts at commercial banks -- increases as the pace of economic activity quickens. Monetary experts have been surprised that money supply growth has been flat just as the economy was showing a burst of strength.

The latest drop, for the week ended Jan. 10, was from an upward revised figure of $362.3 billion for the previous week.

A broader measure of money, M-2, which includes time deposits at commercial banks, also dipped last week. At $870.3 billion, M-2 in the last three months has been growing at less than a 3 percent annual rate, far below Fed targets.

Federal Reserve officials are uneasy at what appears to be a widening discrepancy between the growth in GNP, which shot up at a 6.1 percent annual rate in the fourth quarter, and monetary growth. A slowdown in the expansion of money often has been followed by an economic slowdown.

The Fed gradually raised key short-term interest rates during the first three-quarters of 1978 in an effort to hold down the money supply whiel trying to bolster the dollar abroad.

Until early November, when interest rates were given a further sharp boost as part of the dollar rescue package of policy changes, the Fed seemed to be having little success. Now officials are begining to worry they are having too much.

"This can't continue indefinitely," declares Federal Reserve Gov. Charles Partee. "Either this lag in the money supply is telling us something about the economy or else the strength of the economy will soon lift the demand for money."

Some economists fear it may be forecasting a very sharp drop in the economy, which is not what the Fed wants.

Meanwhile, in the fourth quarter, the difference between the growth of money and the economy reached proportions so great that the velocity of money -- the frequency with which each dollar gets used -- probably reached heights last seen in the 1950s, say some experts.