  In hep-th/9506151 we started a programme devoted to the systematic study of
the conformal field theories derived from WZW models based on nonreductive Lie
groups. In this, the second part, we continue this programme with a look at the
N=1 and N=2 superconformal field theories which arise from both gauged and
ungauged supersymmetric WZW models. We extend the supersymmetric (affine)
Sugawara and coset constructions, as well as the N=2 Kazama--Suzuki
construction to general self-dual Lie algebras.
