Haefliger studied in Zürich, in Geneva, and with Julius Patzak in Vienna.
His 1942 debut in Geneva set the pattern for his career: he sang the evangelist in Bach's St. John's Passion, and it was as
a Bach interpreter that he gained world-wide renown. His second, almost equally successful specialty were lieder. Opera was
only the third, but he was still famous for his Mozart interpretations. 20th century music was another field in which
Haefliger excelled (Orff, Martin, Schönberg).
As an opera singer, he was a member of the Zürich opera from 1943 to 1952, and of the Deutsche Oper Berlin from 1952 to
1974; but he sang in fact all over the world.
From 1971, he was a professor at the Munich academy of music.