Born in Bensberg, Kluxen was the son of a teacher. He took up a four-semester teacher training course at the . From 1935 to 1938 he worked as a primary school teacher in Hinterpommern. After the war and his return from British war captivity he studied history, philosophy and German literature at the University of Cologne and the University of Glasgow from 1947. In 1949 he received his doctorate with a thesis supervised by Theodor Schieder on the political thought of Machiavelli (years later, he was a member of the Schieder commission). In 1954, he habilitated at the University of Cologne on Das Problem der politischen Opposition. Entwicklung und Wesen des englischen Zweiparteiensystems im 18. Jahrhundert (The Problem of Political Opposition. Development and nature of the English two-party system in the 18th century.) In 1950 he became professor at the Pedagogical Academy in Bonn and in 1960 at the University of Cologne. From 1961 to 1963 he was founding rector of the Pädagogische Hochschule in Neuss. From 1963 until his retirement in 1979 he taught Medieval and Modern History at the University of Erlangen.
