CHAPEL HILL, N.C. — The N.C.A.A. did not dispute that the University of North Carolina was guilty of running one of the worst academic fraud schemes in college sports history, involving fake classes that enabled dozens of athletes to gain and maintain their eligibility.

But there will be no penalties, the organization said, because no rules were broken.

In a ruling that caused head-scratching everywhere except Chapel Hill, the N.C.A.A. announced on Friday that it could not punish the university or its athletics program because the “paper” classes were not available exclusively to athletes. Other students at North Carolina had access to the fraudulent classes, too.

Noting that distinction, the panel that investigated the case “could not conclude that the University of North Carolina violated N.C.A.A. academic rules,” the N.C.A.A. said in a statement.

The N.C.A.A.’s determination was a major victory for North Carolina after years of wrangling and uncertainty. The athletic department — one of the most high-profile and lucrative ones in the country, and a source of deep pride in the state — could have faced severe penalties, including the loss of championships in men’s basketball, its signature sport.