The finiteness of homological dimension of complex bordism and cobordism modules of finite CW-complexes ,was proved by Adams [1 ] and Conner-Smith [5 ]. It was proved by Koçak [7 ] that homological dimensions of complex bordism modules of finite-dimensional CW-comp~ lexes are stili finite. We now give some conditions for the finiteness of homological dimension of generalized homology modules of finite - dimensional CW-complexes. In the case of finite CW- complexes the coherence of the coefficient ring and one additional condition (again on the coef- fi cient ring alone) imply the finiteness of homological dimension of generalized homology modules.