Nonreductive WZW models and their CFTs, II: N=1 and N=2 cosets

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.