In the thesis , we define the notion of a state BCK-algebra and a state-morphism BCK-algebra. we present relation between state operators and state -morphism operators and relation between mesure and states on BCK-algebras. We study subdirectly irreducible state(morphism) BCK-algebra. We introduce the concept of an adjoint pair in BCK-algebra and show there is a one-to-one correspondence between adjoint pairs and state morphism oprators.