Composite two-Higgs models (general part)

Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensi ons of the Standard Model. In this approach the dynamical breaking of chira l symmetry occurs in two (or more) channels (near polycritical values for c oupling constants), giving rise to two tar more) composite Higgs doublets. Two types of models are built for which Flavor Changing Neutral Currents (F CNC) are naturally suppressed. In the first Model I the second Higgs double t is regarded as a radial excitation of the first one. In the second Model II the quasilocal Yukawa interaction with Higgs doublets reduces at low ene rgies to a conventional local one where each Higgs doublet couples to a def inite charge current and its v.e.v. brings the mass either to up or to down -components of fermion doublets. For the special configuration of four-ferm ion coupling constants the dynamical CP violation in the Higgs sector appea rs as a result of complexity of v.e.v. for Higgs doublets.