We consider the effective quasilocal quark model with two composite Higgs doublets in strong coupling (polycritical) regime below the chiral symmetry breaking energy scale $\Lambda_{CSB}$. The two-point correlators of scalar and pseudoscalar Higgs fields are calculated. The adjustment of their asymptotics at high energies allows to implement the chiral symmetry restoration in correspondence to the operator product expansion in QCD-like (technicolor, topcolor) models. The requirement of chiral symmetry restoration (CSR) at high energies above the $\Lambda_{CSB}$ yields some bounds on parameters of (composite) Higgs particles and underlying effective quasilocal quark models.