A multiperipheral model, based on one-pion-exchange dominance of low-momentum-transfer processes, is used to study the dynamical origin of the leading Regge trajectories which are coupled to the two-pion system. A Bethe-Salpeter technique is used to calculate the leading singularities in the angular-momentum plane from an input interaction that is determined by the observed low-energy pion-pion scattering amplitude plus the high-energy contribution of the Pomeranchon. The solution results in a p