A parade of major banks marched the prime lending rate up to 8 3/4 percent yesterday, following the lead of Citibank, which initiated the latest quarter-point rise in the closely watched interest rate.

The move depressed both the stock and bond markets which in recent days have worried about a possible credit crunch later this year or early in 1979 as interest rates continue to rise.

The last time the prime stood at 8 3/4 percent was in February 1975.

The latest increase comes three weeks after the last 1/4 point hike in the prime got underway, and six weeks after the previous increase. The prime started the year at 8 percent and stayed there until late April.

Citibank is the second largest bank in the country and sets its prime rate based on a formula of 1 1/4 percent above the three-week moving average for 90-day commercial paper.

But a Citibank spokesman admitted that, under this calculation, the bank was 0.02 percent shy of another required increase. "But when the trend is clearly evident, we go ahead anyway," he explained,

If Citibank had not moved, other banks clearly would have. Within a few hours of Citibank's increase, several dozen sizeable increase, including Chase Manhattan, Chemical, Manufacturers Hanover, and Morgan Guaranty, all of New York; Pittsburgh National. First National Bank of Houston, the Bank of St. Louis and, in California, Bank of America, and Security Pacific.

The banks cited rising short-term rates and continued strong loan demand for the latest increase.

The sharply rising prime is beginning to be reminiscent of the rapid series of hikes in 1974 when the prime rate - which banks charge their best corporate customers for short-term loans - was finally pushed to an all time high of 12 percent.

But while some concern has recently been expressed about an impending crunch - when rates soar out of control and some borrowers get turned away because the demand for funds exceeds the available supply - most analysts say that there is adequate liquidity in the banking system and that no crunch is in the cards unless the Federal Reserve Board slams down hard on growth in the money supply.

Most predictions are that the prime will not exceed 10 percent in this interest rate cycle, with the peak coming either in the fourth quarter of 1978 or early in 1979.

There was some expectations yesterday that the Fed would move to raise short-term interest rates another notch following the latest money supply report on Thursday which showed no decline, following a near-record one week spurt.

But the Fed, in its market activities, acted to bring downward pressure on the federal funds rate, which it uses as a benchmark for its money market operations, and seemed to indicate it was maintaining the 7 1/2 percent target on the key short-term rate for the time being.

There are, however, predictions that when the federal open market committee meets next Tuesday to evaluate monetary policy, another tightening move will result.

Solomon Brothers, in its weekly report on conditions in the credit markets, said the rate of bank credit expansion so far this year was setting a "worrisome pace." It noted that the seasonally adjusted annual rate of growth for credit during the first five months of 1978 has been about 13 percent, nearly 40 percent larger than the same period last year.

It also noted that "for the first time this year, short money rates have risen to and even above the prevailing federal funds rate."

"To a large extent, this tightening of money market conditions up to and above the fund rate is one indication of the strong and increasing fundamental demand for short-term funds and it will probably contribute to further increases in the funds rate," the analysis said.