The university’s switch to Google-hosted e-mail has gone smoothly, and Mr. Sannier estimates that the school is saving $500,000 a year by not handling e-mail itself. Students, he added, also get more than e-mail. They have access to Google Apps, and thousands of them, he says, now use Google’s Web software for calendars, word processing and spreadsheets.

To be sure, Microsoft is not ceding cloud computing to Google. It is investing heavily in huge data centers and Web software. Inside Microsoft, there are engineers and product managers who sound a lot like Googlers.

Ellie Powers-Boyle, 25, a graduate of M.I.T., works on Microsoft’s Web e-mail products. In the last three years, she says, there have been a dozen significant upgrades of the Web e-mail product, and she has worked on three or four new features each time. “We iterate quickly,” she says. “For someone of my generation, the whole idea of waiting years to see if you made the right product makes no sense.”

The challenge for Microsoft is not the ability to do much of what Google does. Instead, the company faces a business quandary. The Microsoft approach is largely to try to link the Web to its desktop business  “software plus Internet services,” in its formulation. It will embrace the Web, while striving to maintain the revenue and profits from its desktop software businesses, the corporate gold mine. That is a smart strategy for Microsoft and its shareholders for now, but it may not be sustainable.

Assuming that competition heats up, Office may continue to be an outstanding product, but Microsoft may not be able to charge as much for it  just as low-cost personal computers eventually undercut the mainframe business, and traditional publishing and media companies have grappled with Internet distribution. The traditional products remain popular, but they become much less profitable.

FOR its part, Google faces its own set of challenges: competition from Microsoft and from Web-based productivity software being offered by start-ups like Zoho and Transmedia as well as more established players like Yahoo. A recent report by the Burton Group, a technology research firm, concluded that it was “unclear at this point whether Google will be able to capitalize on the trends that it’s accelerating.”

Is Google “really committed to the productivity of information workers?” asks Chris Capossela, a vice president in Microsoft’s Office group. “Boy, there’s no question that we are. No customer on the planet thinks about Microsoft without thinking about Office. It’s part of the DNA of Microsoft.

“Needless to say, we are going to do everything we can to remain the leader in this space,” he adds. “And whoever comes our way, we’ll certainly be waiting for them.”