  We prove the unitarity of the Euclidean nonlocal scalar field theory to all
perturbative orders in the loop expansion. The amplitudes in the Euclidean
space are calculated assuming that all the particles have purely imaginary
energies, and afterwards they are analytically continued to real energies. We
show that such amplitudes satisfy the Cutkowsky rules and that only the cut
diagrams corresponding to normal thresholds contribute to their imaginary part.
This implies that the theory is unitary. This analysis is then exported to
nonlocal gauge and gravity theories by means of Becchi-Rouet-Stora-Tyutin or
diffeomorphism invariance, and Ward identities.
