In this paper we generalize the concept of Koliha-Drazin invertible operators by introducing generalized Drazin-ց-meromorphic invertible operators. A bounded linear operator T on a Banach space X is said to be ց-meromorphic if every non-zero point of its spectrum is an isolated point. For T we say that it is generalized Drazin-ց-meromorphic invertible if there exists a bounded linear operator S acting on X such that TS = ST, STS = S, TST − T is ց-meromorphic, while T admits a generalized Kato-ց-meromorphic decomposition if there exists a pair of T-invariant closed subspaces (M, N) such that X = M⊕N, the reduction Tm is Kato and Tn is ց-meromorphic.