An operator T acting on a Banach space X possesses property (gw) if σa(T) \ σSBF− + (T) = E(T), where σa(T) is the approximate point spectrum of T, σSBF− + (T) is the essential semi-B-Fredholm spectrum of T and E(T) is the set of all isolated eigenvalues of T. In this paper we introduce and study two new properties (b) and (gb) in connection with Weyl type theorems, which are analogous respectively to Browder’s theorem and generalized Browder’s theorem. Among other, we prove that if T is a bounded linear operator acting on a Banach space X, then property (gw) holds for T if and only if property (gb) holds for T and E(T) = Π(T), where Π(T) is the set of all poles of the resolvent of T.