Haefliger was born in Davos, Switzerland and studied at the Zürich Conservatory. He studied with Fernando Capri in Geneva and Julius Patzak in Vienna.
He had a lengthy and extensive international career and recorded many oratorios and operas. Starting in 1971, he taught at the Staatliche Hochschule für Musik in Munich, Germany.
Haefliger died from acute heart failure on Saturday, 17 March 2007, in Davos.