For computer wizards on Wall Street, Monday will be Dec. 29, 1999, a step into electronic time travel that will be studied anxiously around the globe.

After months of preparation, the United States' leading brokers, major exchanges, clearinghouses and depository companies will begin mock trading in the widest-ranging test yet by any industry of how well computers will cope with the transition to the next century.The tests, sponsored by the Securities Industry Association, are designed to help brokers and other key players in the $270 billion industry figure out whether their computer systems are ready to handle trades that will settle on Jan. 3, 2000, the first business day of the new century.

Over the next two weeks, the industry will reset the clocks on the test computers and investigate what might happen to anyone trading stocks, options or corporate and municipal bonds on Dec. 30 and 31, 1999, and Jan. 3 and 4, 2000.

The participants are looking for signs of what is widely known as the millennium bug, the catchall name for a variety of electronic foul-ups that are likely to occur when computers fail to recognize that the first days of the new century come after the last days of the old one. The problem stems from the way many microprocessors and computer pro-grams use only two digits to refer to the year in dates - 98 for 1998, for example.

Many chips and programs do not accept a low number like 00 for the year 2000 or 01 for 2001 as valid dates that follow the 99 for 1999.

What complicates the problem is that computers often react to these unrecognized years in unpredictable ways. Some spew inaccurate data. Others make faulty calculations. Some crash immediately. Others appear to function normally but then cannot be restarted once they have been shut down.

Computer specialists have talked about the millennium problem for decades. But only recently have businesses and public officials begun to recognize how wide-ly dates are used in computing and to take seriously warnings that the dawn of the new century could see widespread disruptions in daily life, at the very least, and deadly accidents or perhaps a global economic recession if the millennium problem is not tamed.

Because the securities industry is the first to conduct tests involving connections between many computer users and is publishing vast amounts of information about the results on its World Wide Web site (www.sia.com), year 2000 experts say that the results of these tests could end up having a huge effect on morale in the rapidly growing legions of specialists working on the problem.

"It's good that they are setting a standard of openness for the entire corporate sector," said Edward Yardeni, chief economist of Deutsche Bank Securities. Yardeni has become one of the highest-profile year 2000 pessimists, predicting a 70 percent chance of worldwide recession stemming from computer problems related to the millennium.

"If it goes badly, though, corporations may be more reluctant to share information, and more people are going to come around to my view of the risks," Yardeni said.

The securities companies participating in the test - Coopers & Lybrand, J.P. Morgan & Co., Morgan Stanley, Merrill Lynch & Co. and Lehman Brothers - account for about half the trading volume in stocks, bonds, options and other major financial instruments. Each agreed to set up a discrete computer operation to run the tests. In the United States alone, securities companies are expected to spend $3 billion to $5 billion addressing year 2000 and related computer problems.

Yet, when the millennium actually arrives, Wall Street's ability to function will depend not just on the internal systems it began to test today but on the preparedness of markets overseas, where many players offset any bets placed domestically.

What is more, Wall Street's success at ushering in the millennium will also depend heavily on the year 2000 readiness of New York City's power, water and telecommunications utilities, of the elevators leading to the trading rooms and of countless other systems that are beyond its ability to test.