By generalizing and extending some of the earlier results derived by
Manin and by Merkulov, a twistor description is given of four-dimensional
N-extended (gauged) self-dual supergravity with and without cosmological
constant. In particular, superconformal structures are introduced and used
as a starting point to define complex quaternionic, quaternionic Kaehler and
hyper-Kaehler supermanifolds. A supersymmetry generalization of the Penrose
and Ward constructions are presented.