Armin-Gerd spent the early years of his life in a monastery children’s home, later he spent most of his youth in boarding schools. After his parents divorced, his mother married the actor Hans Otto, who, as a stepfather, became Kuckhoff’s main reference person. His stepfather was the first actor in the Prussian State Theater to be murdered by the Nazis in 1933.

His father was a member of the Rote Kapelle resistance movement and was assassinated in 1943 while waiting for his son to come home. Kuckhoff became active in the resistance movement and fought in the French underground during World War II.

After the war he became a member of the KPD and later a member of the SED after the forced union of the two. He was commissioned to set up a theater studies department, which later became an independent university in Leipzig where he served as Rector.

A long-standing friendship connected him with the literary scholar Hans Mayer, with the director Götz Friedrich, and the artistic director of the Komische Oper Harry Kupfer and Bertolt Brecht. During his career he wrote many books and became well known a scholar of Shakespeare, Friedrich Durrenmatt and Soviet Theater. In 1965 he received the Lessing Prize of the GDR and in 1988 the Patriotic Order of Merit in gold.