Abstract: We considered extending  the quasi-effective stability for nearly integrable Hamiltonian systems. We gave  the quasi-effective stability theorems for nearly integrable generalized Hamiltonian systems and Poisson systems under the KAM (Kolmogorov-Arnold-Moser) type non-degenerate condition. Unlike the general Hamiltonian systems, the action variables and angular variables of the generalized Hamiltonian systems and Poisson systems  under discussion could generally have different dimensions.

Key words:  , quasi-effective stability, nearly integrable generalized Hamiltonian system, Poisson system, KAM type , non-degenerate condition