Abstract: The present paper deals with the persistence of lower dimensional tori, the integrable system has a more general form. By intr oducing a KAM iterative scheme, we set up a KAM-type theorem and proved that the majority lower dimensional tori are not destroyed by the perturbation, the survived tori might be elliptic, hyperbolic, or a torus containing elliptic and hyperbobic ones.

Key words: Hamiltonian system, lower dimensional tori, KAM-type theorem