CONSTRUCTION OF BRST INVARIANT STATES IN G H WZNW MODELS/

We study the cohomology arising in the BRST formulation of G/H gauged WZNW models. We will derive for a general simple group H with arbitrar y representations and levels, conditions for which the cohomology is n on-trivial. We show, by introducing a small perturbation due to Jantze n, in the highest weights of the representations, how stares in the co homology, ''singlet pairs'', arise from unphysical states, ''Kugo-Ojim a quarters'', as the perturbation is set to zero. This will enable us to identify and construct states in the cohomology. The ghost numbers that will occur are +/-p, with p uniquely determined by the representa tions of the algebras involved. Our construction is given in terms of the current modes and relies on the explicit form of highest weight nu ll-states given by Malikov, Feigen and Fuchs.