  We consider a class of $N=2$ supersymmetric non--unitary theories in
two--dimensional Minkowski spacetime which admit classical solitonic solutions.
We show how these models can be twisted into a topological sector whose
energy--momentum tensor is a BRST commutator. There is an infinite number of
degrees of freedom associated to the zero modes of the solitons. As explicit
realizations of such models we discuss the BRST quantization of a system of
free fields, while in the interacting case we study $N=2$ complexified twisted
Toda theories.
