Suppose X is a simply connected mod p loop space such that the mod p cohomology H (X) is finitely generated as an algebra, We show that if X is a C_n- space in the sense of Williams then X is the total space of a C_n-fibration over a finite C_nspace. By using this result, we can reduce problems about C_n-fibration over a finite Generated cohomology to the case of finite C_nspaces. In particular, we give classi- Fication theorems for C_2-spaces and C_p-spaces with finitely generated cohomology.
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