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)−" are automorphisms. This paper generalizes results of Glauberman[3], Kist[8] and Kreuzer[9].