  The twisted G/H models are constructed as twisted supersymmetric gauged WZW
models. We analyze the case of $G=SU(N)$, $H=SU(N_1)\times ...\times
SU(N_n)\times U(1)^r$ with $rank\ G =\ rank\ H$, and discuss possible
generalizations. We introduce a non-abelian bosonization of the $(1,0)$ ghost
system in the adjoint of $H$ and in G/H. By computing chiral anomalies in the
latter picture we write the quantum action as a decoupled sum of ``matter",
gauge and ghost sectors. The action is also derived in the unbosonized version.
We invoke a free field parametrization and extract the space of physical states
by computing the cohomology of $Q$ , the sum of the BRST gauge-fixing charge
and the twisted supersymmetry charge. For a given $G$ we briefly discuss the
relation between the various G/H models corresponding to different choices of
$H$. The choice $H=G$ corresponds to the topological G/G theory.
