The American Football League did not play an All-Star game after its first season in 1960, but did stage All-Star games for the 1961 through 1969 seasons.  All-Star teams from the Eastern and Western divisions played each other after every season except 1965.  That season, the league champion Buffalo Bills played against a team made up of all-stars from the other teams.
        Because the games were played at the end of the season, they occurred in the next calendar year.  Thus, the 1961 AFL All-Star game (with players selected as all-stars for the 1961 season) was played on January 7, 1962; the 1962 game was played in January 1963, etc.
         The link below will take you to an excellent summary of the 1962 AFL All-Star Game, by Mark Bolding.