In this paper, we prove a generalization of Hyers’ theorem on the sta-bility of approximately additive mapping and a generalization of Badora’s theorem on approximate ring homomorphism. We also obtain more general stability theorem, which gives stability theorems on Jordan and Lie homomorphisms. The proofs of the theorems in this paper are given following essentially the Hyers-Rassias approach to the stability of the functional equations connected with Ulam’s problem.