  We calculate generalized parton distribution functions in a field theoretic
formalism using a covariant Bethe-Salpeter approach for the determination of
the bound-state wave function. We describe the procedure in an exact
calculation in scalar Electrodynamics proving that the relevant corrections
outside our scheme vanish. We extend the formalism to the Nambu--Jona-Lasinio
model, a realistic theory of the pion. We go in both cases beyond all previous
calculations and discover that all important features required by general
physical considerations, like symmetry properties, sum rules and the
polynomiality condition, are explicitly verified. We perform a numerical study
of their behavior in the weak and strong coupling limits.
