The recession and the sharp decline in short-term interest rates are putting life back into the bond market, given up for dead only a few months ago.

In recent weeks corporations have flocked to the market to sell long-term and intermediate-term debt securities, using much of the billions of dollars of proceeds to repay more costly borrowings obtained earlier.

And bond buyers, whether retail customers or giant institutions like pension funds and insurance companies, are buying again. Two months ago a company found it difficult to sell a 10-year bond and nearly impossible to sell one that matured in 20 or 30 years, even at interest rates approaching 17 percent.

"There's nothing a bond market likes better than the prospect of the economy entering a period of decline," observed Andrew Morse, of the big brokerage firm Drexel Burnham Lambert Inc.

"As long as investors were concerned that we were going to avoid a steep recession, they were not interested in buying bonds," said James Kochan of Merrill Lynch Pierce Fenner & Smith Inc. "Short-term interest rates could rebound very sharply. If there was that possibility, it was foolish to buy long bonds" that would lock investors into rates well below what they could earn in short-term investments such as 90-day Treasury bills or money market mutual funds.

In October about $2.9 billion of intermediate and long-term bonds were sold, with most of the sales in the 10-year area. Last week alone more than $4.5 billion of longer-term corporate debt offerings were announced, up sharply from the $1.5 billion the week before, according to Neal Garonzik, vice president of the investment banking firm of Morgan Stanley & Co.

While investment bankers--the intermediaries between the companies or governments selling debt and the individuals or institutions buying it--claim always to be busy, they have been overwhelmed by companies seeking to sell bonds in the last few weeks.

"The pace has been very, very grueling," said Garonzik. "We've seen some pretty big names" announcing plans to sell long-term debt, he said.

Among the major firms announcing long-term debt offerings have been E.I. du Pont de Nemours & Co., International Business Machines, Sears Roebuck & Co., Caterpillar Tractor, BankAmerica Corp., and Wells Fargo. General Motors said last week it plans to borrow $5.5 billion, much of it in intermediate-term debt.

One company that plans to convert short-term debt into long-term debt is Du Pont. The Delaware chemicals giant plans to sell about $1 billion of long-term debt this month alone, most of it to repay bank loans it took out last summer to buy Conoco Inc. Du Pont borrowed nearly $4 billion to buy Conoco in the largest corporate merger on record. Like most other short-term debt, those loans carry interest rates that fluctuate up and down with the market.

Even though buyers are back in the bond market and companies again are having luck selling long-term securities, interest rates on those securities remain exceptionally high by any historic measure, although they are down from a month ago.

Most corporations face paying interest rates of 15 to 16 percent for a long-term bond (of, say, 20 to 30 years). The federal government, supposedly the world's premier credit risk, is paying between 12 and 13 percent for its long-term money.

Short-term interest rates--from interest charges on overnight loans like federal funds to 90-day certificates of deposit and Treasury bills--have declined more substantially than long-term rates. Several months ago, short-term rates were higher than long-term rates; thus few investors found it worthwhile to take the risk of lending long-term at 17 percent when they could lend short-term for 19 or 20 percent.

But short-term interest rates have plummeted.

The Federal Reserve, the nation's central bank, had been riding herd on the money supply to keep inflation from rising. That stringent monetary policy helped keep short-term rates near 20 percent even when the rate of inflation had dropped to less than 10 percent.

In the last few months, however, the Fed has allowed short-term rates to fall, in large part because money growth has slowed substantially and also because it does not want to aggravate the recession.

The federal funds rate, the interest charge most susceptible to the Fed's monetary policy maneuvers, has fallen from about 19 percent to 13 percent in the last several months. Other short-term rates have taken a relatively similar tumble.

The prime rate, the key rate on which banks base interest charges for short-term business borrowers, has fallen from 20 1/2 percent to 16 percent in the last two months and is expected to decline further in the weeks ahead.

Now long- and short-term interest rates are back to their normal relationship. As a result, said Morgan Stanley's Garonzik, normal buyers of fixed-income securities such as bonds "no longer have the luxury of staying short. They are trying to lock up prevailing rates."

Bonds usually carry a fixed interest rate that is paid on the face value of the bond. If a bond has a 10 percent interest rate, a $1,000 bond will yield an investor $100 a year. If interest rates rise, the price of the bond will fall. If interest rates fall, the price of the bond will rise. Such price changes keep the yields of outstanding bonds in line with those on new issues.

In the last four weeks, according to Drexel Burnham's Morse, bond prices have risen on average $150 for each $1,000 of face value. Some bonds, like the key 30-year bond from the U.S. Treasury, have risen even more.

Some investors and analysts worry that so many corporations will decide to sell long-term securities that the competition will force long-term rates back up. So far, however, that has not happened, and analysts are confident that the bond market can handle even more new issues before a serious oversupply problem develops.

If the recession continues to be as serious as most economists and investors now believe it is, short-term rates will continue to decline because companies will need less money to finance inventories and long-term rates will continue to be attractive to potential investors.

Some companies are holding off going to the bond market in the expectation that long-term rates will be lower still in a month or two. With short-term rates subsiding, some corporate treasurers find it prudent to hold off locking themselves into a 15 percent payout over many years when they might be able to obtain 14 percent or 13 percent in late December or early January, investment bankers said.

If many companies refrain from floating bonds because lower short-term rates give them the flexibility to wait for lower long-term rates, the prospect of indigestion in the bond market will be slim.

Even Henry Kaufman, the chief economist at Salomon Brothers and one of the leading pessimists about the future of interest rates, said the bond rally is likely to continue for a while. But, he said, based on previous declines in interest rates since the end of World War II, "one might conclude that the current rally is more than two-thirds over in some sectors of the bond market."