Summary: Weyl's theorem for a bounded linear operator \(T\) on complex Banach spaces, as well as its variants, a-Weyl's theorem and property (w), in general is not transmitted to a perturbation \(T + K\), even when \(K\) is a ``good'' operator, such as a commuting finite rank operator or a compact operator. Weyl's theorems do not survive either when \(K\) is a commuting quasi-nilpotent operator. In this paper, we discuss some sufficient conditions for which Weyl's theorem, a-Weyl's theorem as well as property (w) are transmitted under such kinds of perturbations.