Jüssen grew up in Husum. After graduating from a commercial high school, he completed an apprenticeship as a bank clerk. He then went to acting school in 1962. From 1963 to 1965 he had an engagement at the Freie Volksbühne Berlin. In 1965 he founded his Berlin Tournee Theater, which he had to close after 17 performances. From 1967 he worked as a cabaret artist at the Renitenztheater in Stuttgart. From 1969 until its temporary dissolution in 1972, he was a member of the Munich Laughing and Shooting Society along with Dieter Hildebrandt, Klaus Havenstein, Jürgen Scheller and Ursula Noack. He appeared on theater stages in Hamburg, Cologne and Düsseldorf and made 24 theater tours. Jüssen played in tabloid plays as well as in serious plays by, among others, William Shakespeare, Tom Topor, Friedrich Schiller, Wolfgang Borchert and Molière. From 1976 to 1977 he embodied the work-shy lover Adolar von Scheußlich in the ARD slapstick series Klimbim. In 1990 he starred in the comedy series The Dear Relatives. From May 2004 he went on a guest performance tour with the old Klimbim ensemble with the piece he wrote The Klimbim Family Lives, during which 320 performances were given. Jussen has had guest appearances on many television series, including Derrick, Homicide and Florida Lady. He wrote screenplays for Dieter Hildebrandt's Notes from the Province, among others. From 2001, Jüssen appeared as "Prussian on duty" twice a year with the Chiemgauer Volkstheater in TV recordings by Bavarian Radio. Jüssen was the recipient of the Adolf Grimme Prize and also appeared as a book author. His third novel Joseph Satan was published in February 2007. He received the Brothers Grimm Prize from the State of Berlin for his children's theater play Kaspar and the Lion Poldi. He made a stage version of Gerhart Hauptmann's novella Wanda and adapted plays by Shakespeare, Molière and Ben Jonson. Jissen was married to the pop singer Lena Valaitis from 1979 and had a son with her. He last lived in Munich. Since the end of 2007, Jissen, who was a heavy smoker for 45 years, suffered from lung cancer, from which he succumbed on November 10, 2008. His grave is in the Grünwald Forest Cemetery near Munich.