An approach is introduced for dealing with effective theories of hadron scattering at the resonance energies. It allows one to separate the set of independent renormalization prescriptions in those theories and leads to the infinite number of constraints for the allowed physical values of the amplitude parameters, thus giving a possibility to make numerical predictions. The results of comparison with the known data on $\pi\pi$, $\pi K$ and $\pi N$ elastic scattering are shown.