He authored the book Beyond Technique with Fred Fehl, as well as co-authoring with Lillian Moore "Bournonville and Ballet Technique: Studies And Comments On August Bournonville's Etudes Choregraphiques,". He was the subject of the book "Erik Bruhn: Danseur Noble" by John Gruen.
Erik Bruhn met Rudolf Nureyev, the celebrated Tatar dancer, who was on a tour in Denmark. Bruhn became Nureyev's lover, his closest friend, and his protector for many years.
He was director of the Swedish Opera Ballet from 1967 to 1973 and the National Ballet of Canada from 1983 to 1986. A posthumous film biography, "I'm the same only more," by Danish filmmaker Lennart Pasborg won a Cannes award for use of archival material.
His death in 1986 was attributed to lung cancer. However, according to Pierre-Henri Verlhac (Nurejew. Bilder eines Lebens), he may have died of AIDS.