Halligan was born in Troy, New York. He was BS&T's trombonist on their first album, Child Is Father to the Man. When Al Kooper left the band after that first album, Halligan began playing other instruments including piano, organ, and flute. He received a Grammy Award for Best Instrumental Performance for "Variations On A Theme By Erik Satie" from the album Blood, Sweat & Tears. Halligan also arranged many of the band's charts during this time period, and he wrote several songs including "Redemption" and "Lisa Listen To Me." Halligan left BS&T in 1971 after recording their fourth album, when the band began to shift to more rock-oriented music.
In the 1970s and 1980s Halligan composed and arranged music for a number of motion pictures, television, and commercials.
As of 2006 he is active as a composer and performer for various types of music, including jazz and chamber music. In 2011 and 2012 he has been developing and performing an autobiographical one-man show entitled Musical Being. An early title for it was Man Overboard.