  By generalizing and extending some of the earlier results derived by Manin
and Merkulov, a twistor description is given of four-dimensional N-extended
(gauged) self-dual supergravity with and without cosmological constant.
Starting from the category of (4|4N)-dimensional complex superconformal
supermanifolds, the categories of (4|2N)-dimensional complex quaternionic,
quaternionic Kaehler and hyper-Kaehler right-chiral supermanifolds are
introduced and discussed. We then present a detailed twistor description of
these types of supermanifolds. In particular, we construct supertwistor spaces
associated with complex quaternionic right-chiral supermanifolds, and explain
what additional supertwistor data allows for giving those supermanifolds a
hyper-Kaehler structure. In this way, we obtain a supersymmetric generalization
of Penrose's nonlinear graviton construction. We furthermore give an
alternative formulation in terms of a supersymmetric extension of LeBrun's
Einstein bundle. This allows us to include the cases with nonvanishing
cosmological constant. We also discuss the bundle of local supertwistors and
address certain implications thereof. Finally, we comment on a real version of
the theory related to Euclidean signature.
