The present paper is concerned with the notions of Lipschitz and as-ymptotic stability for perturbed nonlinear differential system knowing the corre-sponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an exten-sion of Bihari`s result to Pinto and Pachpatte, and all that sort of things.