It is well known that the set of semi-Fredholm operators is an open semigroup in the set of all bounded linear operators on Banach spaces [3]. Perturbations theorems for semi-Fredholm operators are of great interest (see e.g. [3], [4], [6], [9], [13], [14], [15] and [20]). The main results is a general perturbation theorem for semi-Fredholm operators. Then as a corollary we get some well known results of [6] and [7].