[en] Nonlinear effects related to the polarization properties of high energy γ-quanta produced in collisions between relativistic electrons and an intense laser beam are studied. Exact formulas for the Stokes parameters are found by taking into account nonlinear effects. The respective expansions in the parameter x²/(1+x²), xsup(2)=-esup(2)Asub(μ)sup(2)/msup(2) are found for the first and second harmonics (Asub(μ), is the electromagnetic potential of the laser wave, m is the electron mass). The polarization characteristicu of the γ-quanta produced in the inverse Compton effect are found as depending on the polarization states of the collidine particles (the laser protons n this/ case are circularly polarized). It is shown that the circular polarization of γ-quanta produced in the absorption of tWo laser wave photons exceeds the γ-quantum circular polarization occurring in ordinary Compton scattering