Bond prices, which began to rally Monday afternoon, continued to show gains today, mainly because investors are becoming convinced that the economy is heading for another nose-dive that will reduce interest rates and inflation. i

"The market is starting to anticipate those developments now," according to Bernard Harmon of Drexel Burnham Lambert Inc., a major brokerage firm. t

Bond prices were up about $10 on a face value of $1,000 (or about one point, in the parlance of Wall Street). However, Harmon said prices had been up as much as $20 in earlier trading. But "on the whole, the bond market was generally better," he said. "It had a nice tone."

The stock market had a nice tone, too. The Dow Jones industrial average climbed 20.90 points to 964.93, the most it has gained in one day in about six months.

Although the prospect of a renewed recession would be bad news for corporate profits and, therefore, stock prices, stock investors seemed to hang only on predictions that interest rates would decline by the end of the year, a statement by Reagan officials that the president-elect believes the federal budget can be pared by 6 percent and one by House Speaker Thomas P. ("Tip") O'Neill that President Carter would veto any tax cuts passed by the lame-duck session of Congress.

Nearly all investors and Wall Street professionals believe that a tax cut might be inflationary but that federal spending cuts would be good for the fight against inflation.

While stock prices surged in late trading, bond prices declined. However, over the last several days, bond prices remained up sharply.

Last Friday, for example, the Treasury sold 30-year bonds at an average yield of 12.81 percent. Because the bonds carried a fixed interest rate of 12 3/4 percent on face value, they sold at a slight discount from face value. Today those bonds were yielding 12.30 percent and selling at a premium.

A bond with a face value of $1,000 cost the investor about $1,035 late today, according to Peter Goldsmith of Merrill Lynch, Pierce, Fenner & Smith.

"That's not a bad appreciation over a couple of days," Drexel's Harmon said.

Harmon said the volatile bond market still remains vulnerable to bad economic news -- such as a big increase in the money supply -- although he said that the market already expects the Federal Reserve to increase the discount rate, the interest it charges member banks to borrow from it. The discount rate, now 11 percent, is sharply below market interest rates.

Besides the anticipated economic slowdown, Harmon said there remains a widespread conviction among bond market investors that the Reagan administration "is somehow going to pull off a lesser inflation rate," although the emotional reaction of both the stock and bond markets to the Reagan election has dissipated.

Because bonds carry fixed interest returns, their prices are sensitive both to interest rates and inflation rates.