  We consider a system consisting of a quantum, massless, real scalar field, in
the presence of nonlinear mirrors: infinite parallel planes, upon which the
field satisfies nonlinear boundary conditions. The latter are implemented by
non-quadratic interaction vertices, strictly localized on the mirrors. By using
the appropriate perturbative expansions, we obtain approximate expressions for
the Casimir energy corresponding to weak coupling, regarding the strength of
the interaction terms. We also comment on an alternative expansion scheme that
may be useful when the weak coupling expansion is not justified.
