  All of the PT-symmetric potentials that have been studied so far have been
local. In this paper nonlocal PT-symmetric separable potentials of the form
$V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$, where $U(x)$ is real, are examined.
Two specific models are examined. In each case it is shown that there is a
parametric region of the coupling strength $\epsilon$ for which the PT symmetry
of the Hamiltonian is unbroken and the bound-state energies are real. The
critical values of $\epsilon$ that bound this region are calculated.
