  We analyse the SU(2)_k WZNW models beyond the integrable representations and
in particular the case of SU(2)_0. We find that these are good examples of
logarithmic conformal field theories as indecomposable representations are
naturally produced in the fusion of discrete irreducible representations. We
also find extra, chiral and non-chiral, multiplet structure in the theory. The
chiral fields, which we construct explicitly in SU(2)_0, generate extended
algebras within the model. We also study the process of quantum hamiltonian
reduction of SU(2)_0, giving the c=-2 triplet model, in both the free field
approach and at the level of correlation functions. For rational level SU(2)_k
this gives us a useful technique to study the h_{1,s} correlators of the
c_{p,q} models and we find very similar structures to SU(2)_0. We also discuss
LCFT as a limit of a sequence of ordinary CFTs and some of the subtleties that
can occur.
