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Summary form only given.Resonators of laser oscillators can be completed by dynamic holographic gratings induced by generating waves in a nonlinear medium. The interest in the self-starting lasers with the nonlinear mirrors is related to their unique properties such as the adaptive correction of thermal distortions, dynamic control of beam parameters, etc. The use of media with giant nonlinear coefficients, such as nematic liquid crystals (NLCs), in these lasers for the formation of nonlinear mirrors is of particular interest. We present the experimental and numerical results of our study of a self-starting laser oscillator with cavity completed by nonlinear refractive index grating induced in a NLC at temperature near (beyond or below) the nematic-isotropic phase transition point.