  In this paper we study an N=1 supersymmetric extension of a perturbatively
super-renormalizable (nonlocal)theory of gravity in four dimensions. The
nonlocal supergravity theory is power-counting super-renormalizable and tree
level unitary with the same particle content of the local N=1 supergravity (as
simple example, unitarity of the three dimensional N=1 and N=2 supergravity is
proved). We believe that extended SO(N) supergravity, for N=4 or N=8, might be
free from divergences also at one loop. The extended supergravities would then
result finite at any order in the loop expansion.
