As a young adult, he played a lead role in the 1957 Broadway and 1959 screen adaptations of "Compulsion" and in 1962, Stockwell played Edmund Tyrone in the film version of "Long Day's Journey into Night", for which he won a Best Actor award at the Cannes Film Festival. He appeared in supporting roles in such films as "Paris, Texas" (1984), "To Live and Die in L.A." (1985), "Blue Velvet" (1986), and "Beverly Hills Cop II" (1987). He received further critical acclaim for his performance in "Married to the Mob" (1988), for which he was nominated for the Academy Award for Best Supporting Actor. He subsequently had roles in "The Player" (1992), and "Air Force One" (1997).