Abstract Quantum theory for intracavity parametric nondegenerate four-wave mixing accompanied by cross-phase modulation is presented. A steady-state solution of the Fokker-Planck equation in a generalized P-representation is found. General expressions for arbitrary moments of field operators are derived. Behavior of the second-order auto- and cross-correlation functions as well as of photon number fluctuations is studied. New qualitative quantum phenomena are revealed in the critical region in the presence of bistability.