After 10 days of intermittent failures in a major data network that left thousands of business customers without Internet access, electronic mail and other services, MCI WorldCom Inc. executives said yesterday that the troubled system is up and running and offered to provide 20 days of free service to victims of the outage.

In a telephone conference call yesterday, MCI WorldCom's president and chief executive, Bernard J. Ebbers, apologized to the almost 3,000 customers affected by the costly service breakdown.

Among the major casualties was the Chicago Board of Trade, which lost about four days of service in which 150,000 to 200,000 trades might have been made, valued at anywhere from a few thousand to a several hundred thousand dollars each.

Telecommunications analysts said the incident highlighted the importance--and the vulnerability--of such Internet-based networks, used increasingly by companies to handle important business communications and transactions. "The bottom line is, this could happen to anybody," said Jennifer Pigg, an analyst with the Yankee Group in Boston, recalling a similar outage AT&T Corp. experienced last year.

The embarrassment suffered by MCI WorldCom will apparently exceed the immediate financial consequences of the outage, which will be slight, Ebbers said.

Ebbers said he and his staff have begun writing letters of apology and explanation to affected customers, which include companies as large as America Online Inc. of Dulles and small businesses with only a thousand dollars in monthly revenue.

Many analysts and customers say the effort is too little too late in the aftermath of a problem that first surfaced Aug. 5.

"This thing has gone from unbelievable to unbearable to now unforgivable," said Ken McGee, an analyst with the Gartner Group Inc., a Stamford, Conn., market research company.

"They were not nearly as forthcoming with information as they should have been," Pigg said.

For MCI WorldCom, "the real damage that will occur is MCI customers not renewing," McGee said.

No customers have canceled service, MCI WorldCom executives said.

Earlier this month, MCI WorldCom began having problems with its frame-relay network, one of several kinds of networks providing high-speed Internet access and e-mail service to businesses. The Clinton, Miss.-based company traced the problem to recently installed software from Lucent Technologies Inc. but is still trying to find the exact cause.

Over the weekend, the company shut down the affected network for 24 hours to remove the software, which was being installed to expand the network's capacity for additional customers and services. An older version of the software is now in place.

Despite being back online, customers are still coping with the incident.

"The biggest loss . . . is the trading opportunities that we just can't recover," said Chicago Board of Trade spokesman Bret Gallaway.

Gallaway said the board is considering seeking an alternative vendor and noted that its board president, Thomas R. Donovan, had met with MCI WorldCom executives before the outage to discuss ongoing customer service concerns.

"This wasn't just a failure of MCI WorldCom technology," Gallaway said, "it was a failure for MCI WorldCom customer service as well."

Sean Donelan, a senior network architect for St. Louis-based Data Research Associates Inc., a company that provides Internet service to 3,000 public libraries, agreed. He said the 20 days of free service, which MCI WorldCom will credit to customers' accounts, "is better than nothing," but he has discussed further compensation with his MCI WorldCom sales account team.

Donelan said his sales team did not appear to have any more information than he did during the 10-day period.

In the conference call, Ebbers stated that Lucent "has assumed full responsibility," for the software problem.

Lucent spokesman Bill Price said his company "deeply regrets our role in the recent network problems" but added that "this problem has never happened before," despite numerous installations for other clients.

Ebbers would not discuss whether MCI WorldCom would seek financial compensation from Lucent.

Pigg said the outage should alert customers to the need to provide backup systems for use if networks fail. But Donelan said selling consumers on the idea of backup is difficult. "You try to explain how your network is reliable, and then you try to explain to them why they should have a backup," he said. "They think you're trying to sell them something they don't need, that undercoating for the car."

CAPTION: MCI WorldCom chief Bernard J. Ebbers apologized to the almost 3,000 affected customers.