He was particularly known for his efforts on restoration of papyrus fragments from the ancient Roman town Herculaneum.
[1] He was a resistance member during the German occupation of Norway, and was arrested in May 1942 and incarcerated at Møllergata 19 and at the Grini concentration camp until June 1944.
[2] While incarcerated at Grini, Kleve met co-prisoner and professor of classical philology Eiliv Skard, who gave him lessons in the Latin language.
Subject for his doctorate studies was the understanding of gods in the school of philosophy called Epicureanism, including the philosophical work De natura deorum by the Roman orator Cicero.
[4] Kleve was married to Ragnhild Abusdal from 1951 to 1952, to Esther Thylander from 1957 to 1972, to psychologist Kari Aud Ljøstad from 1972, and to professor Liv Jorunn Storstein from 1974 to 1992.