Businesses and government agencies are girding for another crucial Y2K test today as financial markets reopen and many office computers are turned on for the first time in the new year.

After a second day of monitoring computer systems that have been operating through the rollover into 2000, officials said yesterday that they had found no significant problems because of the Y2K programming bug.

President Clinton's top Y2K adviser, John A. Koskinen, said officials "have no reports or indications there will be any significant problems" today, which he called "an important and significant day" for assessing the Y2K readiness of the business world. He cautioned, however, that there likely would be "small glitches."

Reports of minor problems continued to trickle into monitoring stations around the world. A computer at a video rental store in Colonie, N.Y., charged a customer $91,250 for returning a tape 100 years late, forcing owner to recalculate fees by hand, the Associated Press reported. Data-processing systems in Israel and medical equipment in Scandinavia also experienced minor problems. And in South Korea, 900 families near Seoul lost heat for several hours Saturday after a heating system in their apartment complex malfunctioned because of a Y2K error.

With so few Y2K problems encountered, several firms and government agencies decided yesterday to close or scale back monitoring operations. Montgomery County, for example, canceled plans to operate its "command center" today. Koskinen said the U.S. government probably would cease its 24-hour Y2K watch tomorrow.

Although major U.S. financial exchanges open today, the Chicago Mercantile Exchange and the Chicago Board of Trade began electronic trading last night without problems. Stock markets in Kuwait, Egypt, Singapore, Malaysia and Hong Kong also opened yesterday and reported no Y2K computer problems.