Crossing·symmetric, Regge behaved amplitudes of the Veneziano type are constructed for Ps-Ps scattering, where Ps denotes the pseudoscalar meson octet. Factorization of the parent and the first (odd) daughter Regge trajectories is investigated in detail. Several relations for the VgPSPS and the TgPsPs coupling constants which are equivalent to or consistent with the SU(3) symmetry and Okubo's nonet ansatz are obtained, where Vg and Tg denote the vector and the tensor meson nonets, respectively. Positive definiteness of the square of the first daughter-Ps-Ps coupling constant leads to inequalities for the trajectories or the masses which are well satisfied by experiment. Factorization condition for the first daughter trajectories leads to trajectory or mass relations which are well satisfied experimentally. In particular the requirement of the universality for the parent and the first daughter p couplings leads to the broken SU(6) mass relations which have bee~ obtained by Kawarabayashi, Kitakado and Yabuki using Adler's PCAC consistency conditions applied to the Veneziano model. Consequences from the requirement of the PCAC conditions on the 1l-meson processes are discussed briefly.