  By introducing Q^2-dependence in resonance-reggeon "soft" dual models with
nonlinear trajectories, they are extended to "hard" processes, sharing the
property of parton-hadron duality. The resulting object is a two-component
complex function of three variables - s,t and Q^2, reducing to classical dual
models on the mass shell and to deep inelastic structure functions, or Compton
scattering amplitudes - forward and non-forward - otherwise. As a consequence,
the small- and large-x behavior of the structure functions is also related by
duality. This duality relation holds for each o components (diffractive and
non-diffractive for the amplitude or singlet and non-singlet for the structure)
separately.
