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 . Perturbations theorems for semi-Fredholm operators are of great interest (see e.g. , , , , , ,  and ). The main results is a general perturbation theorem for semi-Fredholm operators. Then as a corollary we get some well known results of  and .