Oundjian subsequently studied at the Juilliard School with Ivan Galamian, Itzhak Perlman, and Dorothy DeLay.

While at Juilliard, he minored in conducting, and later received encouragement in his endeavors when he attended a master class from the eminent Austrian conductor Herbert von Karajan.

[2] In 1980, Oundjian won First Prize at the International Violin Competition in Viña del Mar, Chile.

[5] Oundjian was named music director of the Toronto Symphony Orchestra (TSO) in January 2003, and assumed the post in 2004.

[6][13] In January 2011, the Royal Scottish National Orchestra announced the appointment of Oundjian as its next music director, as of the 2012–2013 season, with an initial contract of 4 years.

[18] In September 2024, the Colorado Symphony announced the promotion of Oundjian to the post of its music director, effective with the 2025–2026 season, with an initial contract of four years.

[21][1] In June 2007, Oundjian conducted the world premiere of an oratorio by Idle and John DuPrez based on the Monty Python movie Life of Brian, titled Not the Messiah (He's a Very Naughty Boy), at the first Luminato Festival in Toronto, Canada.