  The effective action of string theory has both bulk and boundary terms if the
spacetime is an open manifold. Recently, the known classical effective action
of string theory at the leading order of $\alpha'$ and its corresponding
boundary action have been reproduced by constraining the effective actions to
be invariant under gauge transformations and under string duality
transformations. In this paper, we use this idea to find the classical
effective action of the O-plane and its corresponding boundary terms in type II
superstring theories at order $\alpha'^2$ and for NS-NS couplings. We find that
these constraints fix the bulk action and its corresponding boundary terms up
to one overall factor. They also produce three multiplets in the boundary
action that their coefficients are independent of the bulk couplings under the
string dualities.
