K-loops have their origin in the theory of sharply 2-transitive groups. In this paper a proof is given that K-loops and Bruck loops are the same. For the proof it is necessary to show that in a (left) Bruck loop the left inner mappings L(b)L(a) L(ab)−1 are automorphisms. This paper generalizes results of Glauberman [3], Kist [8] and Kreuzer [9].