  Among the usual constraints of (1,1) supergravity in d=2 the condition of
vanishing bosonic torsion is dropped. Using the inverse supervierbein and the
superconnection considerably simplifies the formidable computational problems.
It allows to solve the constraints for those fields before taking into account
the (identically fulfilled) Bianchi identities. The relation of arbitrary
functions in the seminal paper of Howe to supergravity multiplets is clarified.
The local supersymmetry transformations remain the same, but, somewhat
surprisingly, the transformations of zweibein and Rarita-Schwinger field
decouple from those of the superconnection multiplet. A method emerges
naturally, how to construct `non-Einsteinian' supergravity theories with
nontrivial curvature and torsion in d=2 which, apart from their intrinsic
interest, may be relevant for models of super black holes and for novel
generalizations in superstring theories. Several explicit examples of such
models are presented, some of which immediately allow a dilatonic formulation
for the bosonic part of the action.
