After studying piano, conducting and composition at Florida State University B.M 1965 with Honors, M.M 1967, he received a doctorate in composition from Ohio State University in 1972. He did additional study in conducting at the Mozarteum, Salzburg, Austria, 1966, computer music at IRCAM, Paris, 1981, and at Stanford University, California, 1984. He was awarded a Fulbright Fellowship/Polish Cultural Grant to work at the Experimental Music Studio of Polish Radio, Warsaw, Poland, 1972 -74.
Montague was born and educated in the US, but lived in Warsaw, Poland (1972–74) on a Fulbright Fellowship, and since 1974 in London working as a freelance composer, pianist, conductor and touring worldwide. His music has been performed at numerous international festivals, including the BBC Proms at the Royal Albert Hall in London, the Warsaw Autumn festival, the Paris Festival d'Automne, the Kennedy Center in Washington, D.C., and the Hong Kong and Singapore Festivals.
He has been commissioned by such sources as the BBC Proms, the Royal Festival Hall (London), the National Portrait Gallery (London), the Royal Ballet (UK), British Telecom (for the London Symphony Orchestra), the Trans Atlantic Arts Consortium (UK/US), the Calgary Philharmonic (Canada), the Hilliard Ensemble, the Smith Quartet (UK), pianist Stephen Kovacevich, percussionist Evelyn Glennie, harpsichordist Elisabeth Chojnacka, and the International Computer Music Association.
As a pianist, he has recorded for many European radio networks and has performed at Carnegie Hall in New York, the Queen Elizabeth Hall in London, and the Centre Georges Pompidou in Paris. In 1985 he formed a duo with pianist Philip Mead, Montague/Mead Piano Plus which tours internationally. His conducting specialty is 20th and 21st century music. In addition, Montague has created multi-channel electroacoustic sound environments in collaboration with the sculptor, Maurice Agis, and composed a number of music theatre works for outside spaces such as his Horn Concerto for klaxon horn and an orchestra of automobiles.
Although a long term British resident (dual national - US/UK since 2000) his compositional influences are transatlantic. He comments: "I have lived in Britain since 1974 but my musical heroes remain American: I admire Charles Ives's unapologetic juxtaposition of vernacular music and the avant-garde, Henry Cowell's irreverent use of fist and arm clusters, the propulsive energy of minimalism, and John Cage's radical dictum that 'all sound is music'. And, like Henry Cowell, I want to live in the whole world of music, not just one corner. I am equally at home writing for a large professional symphony orchestra, chamber groups, dance, music theatre or experimental works, for example, motorcycles, brass, percussion and piano".
In the UK, Montague was a founder of Sonic Arts Network in 1980, served as Chair of the SPNM (Society for the Promotion of New Music) during 1993-97, and was Associate Composer with The Orchestra of St. Johns, Smith Square, London, 1995 - 97. He has been a Guest Professor at the University of Texas - Austin, 1992, 1995, 2000 and at the University of New Zealand in 1997. Recent Composer Portraits of his music have taken place in London, New York, Chicago, Columbus, Houston, Mexico City, Vienna and Budapest.
His awards include first prize at the Bourges International Electroacoustic Music Competition (France) in 1994, the Ernst von Dohnányi Citation for Excellence in Composition in 1995, and the Ohio State University Distinguished Alumnus Award in 2000, Honorary Fellow Trinity College of Music 2001, Fellowship of Leeds College of Music, 2004, and the International Piano Magazine Award: "Best Contemporary Piano Music Recording 2006" for the CD of his piano music Southern Lament on the NMC label (UK).
In addition to his freelance work Montague also teaches composition and orchestration at Trinity Laban Conservatoire of Music and Dance London, and is the New Music Associate at Cambridge University's Kettle's Yard Art Gallery, 2010 -2012 (UK). Publisher United Music Publishers - UMP Composers - Stephen Montague 
- Stephen Montague biography at UMP
- Stephen Montague information at The Living Composers Project
- Aeolian Furies recording