I.B.M. appears on the verge of acquiring Sun Microsystems, a longtime rival in the computer server and software markets, for nearly $7 billion.

The two companies have been negotiating for weeks, ironing out terms of an agreement that would turn I.B.M. into the dominant supplier of high-profit Unix servers and related technology.

I.B.M. is offering $9.50 a share, down from a bid of $10 a share, said people familiar with the discussions who were not authorized to speak publicly. The new agreement would restrict I.B.M.’s ability to walk away from the deal, these people said.

Even at $9.50 a share, the deal would value Sun, based in Santa Clara, Calif., at close to $7 billion. It is close to a 100 percent premium based on Sun’s value before rumors of an acquisition spread last month.