SAN FRANCISCO — Shares of PalmSource Inc., maker of the Palm operating system for handheld computers, surged 78 percent on Friday on news that the Japanese software company Access Co. had agreed to pay $324 million for it.

The news had some analysts wondering how PalmSource, which has failed to excite investors since Palm Inc. spun it off two years ago, could draw such an offer.

"This was really dumb," said Needham & Co. stock analyst Charles Wolf. "They are paying that kind of money for a company with no real profits and one product. I'm stunned."

Access was offering $18.50 for each share of PalmSource common stock, an 83 percent premium to the stock's Thursday closing price of $10.09 on the Nasdaq Stock Market. PalmSource's share price rose $7.89 to close at $17.98 on Friday.

PalmSource has seen its market share erode since its separation from Palm Inc., a darling of the tech investors in the high-flying 1990s. Microsoft Corp. and Symbian have in recent months gained in handheld operating systems.

In June, PalmSource said it was cutting its full-time work force in the U.S. by about 16 percent as it reorganized key departments. At the time, the company posted an operating loss of $700,000, or 4 cents per share, for the fourth quarter, a figure which excluded a $26.7 million gain from the sale of its interest in Palm Trademark Holding Co. to palmOne Inc., the former name of Palm Inc.

Nevertheless, more than 45 companies worldwide have licensed PalmSource software. More than 39 million mobile devices run on the Palm OS.

Access produces the NetFront Internet browser for mobile devices. By acquiring PalmSource, it is positioning itself to offer phone makers more applications as well as the Palm OS, said Forrester Research analyst Charles Golvin.

The problem is that while the Palm OS ran a slew of traditional handhelds, that business is "drying up" Golvin said. The trend in handhelds, says Golvin, is moving towards smartphones.

"I think the questions about PalmSource revolve around growth and future devices," Golvin said. "How much penetration can the Palm OS grab in the future?"