  We investigate and clarify the mutual compatibility of the higher order
corrections arising in supergravity and string theory effective actions and the
non-linear duality symmetries of these theories. Starting from a conventional
tree level action leading to duality invariant equations of motion, we show how
to accommodate duality invariant counterterms given as functionals of both
electric and magnetic fields in a perturbative expansion, and to deduce from
them a non-polynomial bona fide action satisfying the Gaillard-Zumino
constraint. There exists a corresponding consistency constraint in the
non-covariant Henneaux-Teitelboim formalism which ensures that one can always
restore diffeomorphism invariance by perturbatively solving this functional
identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F
and F^4 counterterms in Maxwell theory.
