Because his father worked as a caretaker at the Conservatorio Nacional, Guevara used to eavesdrop on the music dictations that were being given to older children and sometimes ventured to shout the answer before running away.
In 1952, while playing the piano in an orchestra in Guayaquil, he studied composition and the analysis of Bartok's music with the Hungarian musician Jorge Aq.
After twelve years in France, he went back to Ecuador where in 1972 he formed the choir of the Central University of Quito.
He acted as a conductor of the National Symphony Orchestra from 1974–75 and director of the Conservatorio Nacional (1980–88) where he taught composition and the history of Ecuadorian Music.
[1] Mainly nationalist he nonetheless explored contemporary techniques, which led Robert Stevenson to write: "Guevara Viteri has drawn on European styles".