  We derive the N=1 supersymmetric extension for a class of weakly nonlocal
four dimensional gravitational theories.The construction is explicitly done in
the superspace and the tree-level perturbative unitarity is explicitly proved
both in the superfield formalism and in field components. For the minimal
nonlocal supergravity the spectrum is the same as in the local theory and in
particular it is ghost-free. The supersymmetric extension of the
super-renormalizable Starobinsky theory and of two alternative massive nonlocal
supergravities are found as straightforward applications of the formalism.
Power-counting arguments ensure super-renormalizability with milder requirement
for the asymptotic behavior of form factors than in ordinary nonlocal gravity.
The most noteworthy result, common to ordinary supergravity, is the absence of
quantum corrections to the cosmological constant in any regularization
procedure. We cannot exclude the usual one-loop quadratic divergences. However,
local vertices in the superfields, not undergoing renormalization, can be
introduced to cancel out such divergences. Therefore, quantum finiteness is
certainly achieved in dimensional regularization and most likely also in the
cut-off regularization scheme. We also discuss the n-point scattering
amplitudes making use of a general field redefinition theorem implemented in
the superspace. Finally, we show that all the exact solutions of the local
supergravity in vacuum are solutions of the nonlocal one too. In particular, we
have the usual Schwarzschild singularity. We infer that the weak nonlocality,
even in the presence of minimal supersymmetry, is not sufficient to solve the
spacetime singularities issue, although the theory is finite at quantum level.
