  We present a derivation of the N=1 and N=2 superconformal coset constructions
starting from a supersymmetric WZW model where a diagonal subgroup has been
gauged. We work in the general framework of self-dual (not necessarily
reductive) Lie algebras; but even in the reductive case these results are new.
We show that the BRST cohomology of the gauged supersymmetric WZW model
contains the N=1 (and if it exists also the N=2) coset generators. We also
extend the BRST analysis to show that the BRST cohomology of the supersymmetric
WZW model agrees with that of an ordinary bosonic WZW model (in a
representation twisted by the presence of the coset fermions). In particular,
in the case of the topological G/G coset, the supersymmetric and
nonsupersymmetric theories agree.
