Nonlocal supergravity

We propose an $N=1$ supersymmetric extension for a class of weakly nonlocal four-dimensional gravitational theories. The construction is done in the superspace where the off-shell supersymmetry is manifest. The tree-level perturbative unitarity is explicitly proved both in 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 nonlocal Starobinsky theory is found as a straightforward application of the formalism.