Effective many-fermion models with finite momentum cutoff in the regime of dynamical symmetry breaking are considered as low-energy approximation to the action of quantum chromodynamics. The quasilocal interaction vertices responsible for the formation of dynamic fermion mass are classified for these models in the near-critical region of coupling constants. It is shown that in four-dimensional space not only the 4-fermion interaction but also vertices with six and eight fermion fields and any number of derivatives are also important. In the mean field approximation an equation is derived for the critical surface for the coupling constants of the effective fermion action. The role of the leading interaction vertices in forming the physical parameters that do not depend on the momentum cutoff is discussed.