The bootstrap mechanism ofZachariasen andZemach (3) is used to study the resonant scattering of pseudoscalar mesons under the assumption of mass degeneracy and the existence of the vector resonances. The general bootstrap conditions on the mass and the coupling constants are formulated andCapps’ result (6) onSU3 symmetry is rederived from our more general equations. The question of the possible existence of further resonances is reduced to a simple eigenvalue problem. The forces due to the vector exchange are found to be repulsive in the 10,\(\overline {10} \) and 27SU3 channels but attractive in the 1 and 8, and when calculated with the self-consistent parameters are strong enough to bind scalar resonances in the 1 and 8 channels. These resonances may contribute to the interaction forces. Taking into account the scalar octet exchange in addition to the vector exchange we have bootstrapped the two octets together in a double self-consistency calculation. A self-consistent solution is obtained atm v ∼ 1000 MeV,m s ∼ 500 MeV, and a small value for the ratio of the scalar coupling strength to the vector coupling strength (5%). The singlet scalar meson has not been bootstrapped for the sake of simplicity, but we have some reasons to believe that its effect should be small. We have tentatively assigned the weakly coupled K’ (725) to theI=1/2 members of the scalar octet, the K1K1 threshold anomaly to theI=0 member of the octet, and the ABC «particle» to the scalar unitary singlet. Spin 2+ «particles» are also predicted using the self-consistent parameters in the 1 and 8 channels at higher energies, the singlet being here tentatively identified as f0 while the octet occurs at presumably too high energies to be seen. Because of the crudeness of the model, no quantitative significance of the results is claimed, but the model is expected to be qualitatively correct and to give the right orders of magnitude for the various parameters.