In 1943, Haefliger sang for the first time the Evangelist in Bach's St John Passion in Zurich. After this debut he was engaged for several concerts in Switzerland and – after World War II – abroad. He soon won the attention of Ferenc Fricsay, who engaged him for the Salzburg Festival where Haefliger's world career started in 1949 with the role of Terasias in Carl Orff's opera Antigonae. He also sang the role of First Armed Man in The Magic Flute under the baton of Wilhelm Furtwangler in the same year at the Salzburg Festival.
In 1952, he responded to the call of Ferenc Fricsay and joined him at the Deutsche Oper Berlin where he sang the tenor parts in all Mozart operas, in Rossini's The Barber of Seville and Le comte Ory, in Hans Pfitzner's Palestrina, the part of Hans in Smetana's The Bartered Bride, as well as many other tenor parts.
He had a lengthy and extensive international career and recorded many oratorios and operas. From 1971 to 1988, he taught at the Staatliche Hochschule für Musik in Munich, Germany. Haefliger made his Boston debut in 1965 for the Peabody Mason Concert series.
Haefliger also gave master classes in Zurich, Japan and in the United States.