In 1966, Mudra signed a three-year contract to coach the Montreal Alouettes of the Canadian Football League (CFL). They had a 7–7 record in the 1966 CFL season, the team's best finish since 1956. The Alouettes made the CFL postseason, but lost to the Hamilton Tiger-Cats in the conference semi-finals. After one year, Mudra resigned from Montreal to accept the head coaching position for the University of Arizona. The Arizona Wildcats had 3–7 records in the previous two seasons. In Mudra's first year, Arizona went 3–6–1 in 1967. They went 8–1 in 1968, and were invited to the 1968 Sun Bowl, which Arizona lost to the Auburn Tigers. Mudra left Arizona in 1969 for Western Illinois University. The Western Illinois Leathernecks football team had a 2–7–1 record in their previous season. In five seasons from 1969 to 1973, Mudra's Leathernecks had a record. The Leathernecks won the Illinois Intercollegiate Athletic Conference championship in the 1969 season, and appeared in the 1973 NCAA Division II quarterfinals.
