Fermion models with self-interaction, including derivatives of fields, are investigated in the strong coupling regime with several coupling constants matched to their critical values. For the two-channel model, the existence of three phases with different correlation lengths in a scalar channel is established in the vicinity of the tricritical point. For all regions of the phase diagram, the mass spectrum of the composite scalar and pseudoscalar bosons is obtained in the large-log approximation. A phase with dynamic breaking of P-parity is discovered.