  We derive a general expression for the Casimir energy corresponding to two
flat parallel mirrors in d+1 dimensions, described by nonlocal interaction
potentials. For a real scalar field, the interaction with the mirrors is
implemented by a term which is a quadratic form in the field, with a nonlocal
kernel. The resulting expression for the energy is a function of the parameters
that define the nonlocal kernel. We show that the general expression has the
correct limit in the zero width case, and also present the exact solution for a
particular case.
