CompuServe and H&R Block Inc. did not name a bidder, but CompuServe stock has risen sharply this week following market rumors that AOL was thinking of buying the company.

Analysts have said a combination could benefit both companies. AOL needs more equipment to unclog its network bottlenecks, and CompuServe has been losing money amid subscriber defections to rival service providers.

H&R Block, which owns 80 percent of Columbus, Ohio-based CompuServe, had wanted to spin off the online service, but put those plans on hold because CompuServe has been losing money.

CompuServe rose $1.62 to close at $12.62 today on the Nasdaq market. It had gained nearly 19 percent in the previous two sessions. At that price, the company is worth about $1 billion.

America Online, which rose 7.6 percent yesterday on the New York Stock Exchange, fell $1.125 today to close at $44.62.

Strongest with business and professional users, CompuServe failed in an attempt to create a separate service for families and computer novices, the mainstay of America Online's rapid growth.

America Online, based in Dulles, Va., has more than 8 million subscribers and CompuServe has fewer than 3 million. Both offer Inter

net access and proprietary services such as online magazines, forums and chat groups.

Since America Online grew so fast that customers were complaining they couldn't get the unlimited service they were charged for, it could benefit from obtaining CompuServe's resources.

A combined company also might be in a better position to compete with Microsoft Network, the nation's third-largest online service.

CompuServe also is strong in Europe and Japan, where America Online has been trying to expand.

Even if a merger would benefit both companies, it still would face formidable barriers, including the companies' different styles and the need for regulatory approval.

An America Online spokeswoman said the company didn't comment on rumors or speculation.