The consequences of assuming that there is no isospin T=2 part in the commutator [Q̇a5,Q¨b5] of time derivatives of the axial charges Qa5 and Qb5 have been investigated. The superconvergence condition derived from this assumption provides constraints on Weinberg's mass matrix. The mixing angles introduced by Weinberg for the π-A1-ρ-σ system of mesons and for the nucleon resonances belonging to the (1, 1/2 ) and ( 1/2 , 0) representations of the chiral group are now determined. When only ρ-wave pion interactions are considered, it is shown that the new constraints on the mass matrix lead to mass degeneracy for the symmetric representations of SU(2)⊗SU(4). The constraints on the spin spectrum derivable from the superconvergence conditions are briefly mentioned.