[en] We study parity violating states of strongly correlated two-dimensional electronic systems. On the basis of mean field theory for the SU(2N)-symmetric generalization of the system involved we give the arguments supporting the existence of these states at a filling number different from one-half. We derive an effective Lagrangian describing the long wavelength dynamics of magnetic excitations and their interaction with charged spinless holes. We establish that the ground state of a doped system is superconducting and discuss the phenomenological manifestations of the parity violation. (author). 48 refs, 3 figs