  It is known that Ashtekar's formulation for pure Einstein gravity can be cast
into the form of a topological field theory, namely the $SU(2)$ BF theory, with
the B-fields subject to an algebraic constraint. We extend this relation
between Ashtekar's formalism and BF theories to $N=1$ and $N=2$ supergravities.
The relevant gauge groups in these cases become graded Lie groups of $SU(2)$
which are generated by left-handed local Lorentz transformations and
left-supersymmetry transformations. As a corollary of these relations, we
provide topological solutions for $N=2$ supergravity with a vanishing
cosmological constant. It is also shown that, due to the algebraic constraints,
the Kalb-Ramond symmetry which is characteristic of BF theories breaks down to
the symmetry under diffeomorphisms and right-supersymmetry transformations.
