A few months ago, free online courses from prestigious universities were a rarity. Now, they are the cause for announcements every few weeks, as a field suddenly studded with big-name colleges and competing software platforms evolves with astonishing speed.

In a major development on Tuesday, a dozen highly ranked universities said they had signed on with Coursera, a new venture offering free classes online. They still must overcome some skepticism about the quality of online education and the prospects for having the courses cover the costs of producing them, but their enthusiasm is undimmed.

But at universities that have not yet seized a piece of this action, the response ranges from curiosity to fear of losing a crucial competition. When University of Virginia trustees ousted their president last month — a decision they later reversed — one reason cited was concern about being left behind online. (Virginia was included in Tuesday’s announcement.)

“There’s panic,” said Kevin Carey, director of education policy at the New America Foundation, a nonpartisan research group. “Whether it’s senseless panic is unclear.”