  On the base of the quantum kinetic equation for density matrix in plasma at
the stimulated bremsstrahlung of electrons on ions, the nonlinear absorption
rate for high-intensity shortwave radiation in plasma has been obtained within
relativistic quantum theory. Both classical Maxwellian and degenerate quantum
plasma are considered for x-ray lasers of high intensities. Essentially
different dependences of nonlinear absorption rate on polarization of strong
laser radiation is stated.
