We consider 2D gravity coupled toc≦1 conformal matter in the conformal gauge. The Liouville system is represented by a free scalar field,φ L, with background charge such that the BRST operator imposing reparametrization invariance is nilpotent. We compute the cohomology of this BRST charge on the product of the Fock space ofφ L with those of the ghosts and one other free scalar field,φ M representing the matter system. From this calculation the physical states of the full theory are determined. For thec<1 case the further projection from the Fock space ofφ M to the irreducible representation, using Felder's resolution, reproduces the results of Lian and Zuckerman.