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He studied at the Royal College of Music in Stockholm, where he studied piano and violin, and began his musical career as keyboardist who toured with Björn Skifs and on ABBA's world tours.
Eljas worked as a producer for CBS Records International (now Sony Music) During the 1980s, he orchestrated the musical Chess, conducting the London Symphony Orchestra for a recording of the musical and a 1984 European tour. In 1988, Eljas was also one of the orchestrators for the Broadway musical Carrie
From 1978 to 1995, Eljas was often Sveriges Television's band leader for its shows. He was also a regular celebrity contestant on the popular charades show Gäster med gester on TV.
1977: ABBA: The Movie – musician
- 1984 – Chess – arrangements & orchestration
- 1995 – Kristina från Duvemåla – orchestration
- 2017 – Chess – new orchestration (first performed in Kristianstad, Sweden, relaunching the musical globally)
- "About us - The Göteborg Opera". en.opera.se.
- "Anders Eljas Music". www.eljasmusic.com.
- Sheridan, Simon (8 May 2012). "The Complete ABBA (40th Anniversary Edition)". Titan Books (US, CA) – via Google Books.
- "Review/Theater; The Telekinetic 'Carrie,' With Music". The New York Times. 13 May 1988.
- Article in VG 2000-05-31
- Article Se & Hör 2015-12-25