BUDAPEST—Central Budapest's cafes and shops were long closed and its narrow streets quiet at 3 a.m. Sunday, when David Recsey let out a horrified gasp.

The 28-year-old Hungarian stared at his television in disbelief as the Atlanta Falcons' kick returner dodged defenders and ran 102 yards for a touchdown against his favorite National Football League team, the Green Bay Packers. He protested when the Packers, well ahead as time ran low, appeared to court injury by sending quarterback Aaron Rodgers in for more playing time.

"Rodgers is good. The offense is strong," said Mr. Recsey, whose apartment is decorated in Green Bay Packers posters and yellow and green Packers' footballs. "If they keep up this level of play, no one will stand a chance against them."

American football, which for years has struggled to promote itself outside the U.S., has developed an ardent and growing following in former communist countries of Central and Eastern Europe. More than 2,000 Hungarians—including many women—play on more than 20 amateur teams, overcoming shortages of equipment and fields and a general ignorance of the game in a country where soccer is considered the real football.

They include Mr. Recsey, who is also the starting quarterback for the Budapest Wolves. There's also 35-year-old Wolves' wide receive Peter Beran, a former sprinter and New England Patriots follower, and Kata Szaraz, a 29-year-old linebacker on the Wolves' women's affiliate, which plays in the Austrian Ladies' Football League against the likes of the Graz Black Widows.