The generalization of DAMA (dual amplitude with Mandelstam analyticity) to the case of meson-baryon scattering is studied. To this end trajectories with left-hand cut are introduced in the model under consideration. Threshold and asymptotic bounds on these trajectories are obtained. Combinations suitable for boson-fermion and fermion-fermion amplitudes are constructed. A specific example, namely πN-scattering, is considered, for which dual models of invariant amplitudes are constructed.