Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the standard model. In this approach, the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), which gives rise to two (or more) composite Higgs doublets. Two types of models are built for which the flavor-changing neutral currents (FCNC) are naturally suppressed. In model I, the second Higgs doublet is regarded as a radial excitation of the first one. In model II, at low energies, the quasilocal Yukawa interaction with Higgs doublets reduces to a conventional local one where each Higgs doublet couples to a definite charge current and its vacuum expectation value brings the mass either to up- or to down-components of fermion doublets. For a special configuration of four-fermion coupling constants, the dynamical CP-violation in the Higgs sector appears as a result of complexity of the the vacuum expectation value (v.e.v.) for Higgs doublets.