Mexican composer of mostly stage, orchestral, chamber, choral, vocal, and piano works that have been successfully performed throughout the Americas and in Europe; he is also active as a conductor.

Mr. de Elías first studied composition, piano and theory with his father Alfonso de Elías (b. 1902–d. 1984) and was simultaneously active as a chorister with the Sociedad Musical Mozart, studied ancient music and recorder with Roberto Rivera, violin with Daniel Saloma, and organ with Juan Bosco Correro. He then studied cello with Sally van den Berg at the Escuela Nacional de Música and attended a composition workshop with Carlos Chávez at the Conservatorio Nacional de México.

He also attended conducting classes with Edgard Doneux, Luis Herrera de la Fuente and Ernst Huber-Contwig, piano classes with Bernard Flavigny and Gerhart Kämper, electronic music classes with Jean-Étienne Marie (1967–68), and new music classes with Karlheinz Stockhausen (1968–2007). He studied at the Escuela de Filosofía y Letras at the Universidad de Guanajuato in the late 1960s and worked at the Columbia-Princeton Electronic Music Center in 1974, on an invitation from Alfredo Del Mónaco.

He has received the Medalla Mozart (1991) and the Premio Nacional de Ciencias y Artes (1992) and his Sonante No. 11, ‘Bosquejos de una ofrenda’, was the selected work at the Tribuna Musical de América Latina y el Caribe (1995). Most recently, he received the Diploma al Mérito Artístico from the Instituto Superior de Arte, for his entire oeuvre (2001).

He has been a member of the Sociedad Mexicana de Musicología since 1990, of the Académico de Número of the Academia de Artes since 1991 and of the Sistema Nacional de Creadores (in which he is now a Creador Emérito) since 1993. He became a member of the Consejo Consultivo del Festival Internacional Cervantino in 2001 and was made an honorary member of the Unión Nacional de Escritores y Artistas de Cuba in 2001, a rare accomplishment for a non-Cuban.

He is also active in other positions. He founded the Orchestra de Camera Santa Cecilia (1959), the chamber orchestra Amigos de la Música (1960) and the Escuela de Música at the Universidad de Guanajuato and the Grupo Experimental de Música de Cámara at the Escuela de Música de Guanajuato (1965, of which he was also the director). In addition, he was a member of the Grupo Proa for avant-garde composers in the mid-1960s. He also organized the Festival Debussy (1968), worked at the Laboratorio de Música Electrónica at the Conservatorio Nacional de Música (1971) and founded the Instituto de Música at the Universidad Veracruzana (1975, which he also led from 1975–80).

In addition, he founded the Iniciación Musical Infantil courses (1975, now known as the Centro de Iniciación Musical Infantil), the Coro del Instituto de Música (1975, now the Coro de la Universidad Veracruzana), the Orquesta Sinfónica de Veracruz (1980), and the Orquesta Filarmónica de Jalisco (1988). Most recently, he founded the Consejo Mexicano de la Música, which is a member of the UNESCO Music Council (1995, for which he served as president from 1995–98). In addition, he organized the Foro de Compositores del Caribe (1999), served as president of the jury of the Tomás Luis de Victoria Prize (2000) and founded the Colegio de Compositores Latinoamericanos de Música de Arte (2000).

Though initially a pianist, he served as assistant director of the Orquesta Sinfónica de Guanajuato from 1964–68 and to Luis Herrera de la Fuente at the Orquesta Sinfónica Nacional in 1968. He ceased his activities as a pianist to devote his time to composing and teaching in the late 1960s and later went to Brussels on an invitation from Edgard Doneux, with whom he helped to conduct the Chamber Orchestra of the BRTN until 1975. He served as artistic director of the Primer Festival Internacional de Música in Xalapa in 1976.

He served as Director-General of the Área de Artes at the Universidad Veracruzana from 1982-84 and toured Poland as a conductor of various orchestras. He served as artistic director of the Orquesta de Cámara of the Instituto Nacional de Bellas Artes from 1984–86 and conducted the Orquesta Sinfónica de Guadalajara in 1987 and the Orquesta Filarmónica de Jalisco from 1988–90.

During the mid-to-late 1960s, he taught chamber music, composition and piano at the Escuela de Música de Guanajuato. He launched a large academic reformation of the Conservatorio de las Rosas in Morelia in 1990, of which he served as Director-General in 1990-91. He served as director of the Coordinación Nacional de Música y Ópera at the Instituto Nacional de Bellas Artes from 1991 to 93.