The theory for saturated magnetic dipole and electric quadrupole absorption of monochromatic radiation at dipole-forbidden transitions of gas media is developed. It is shown that in the case of quasi-resonant polarizability, when the radiation frequency is close to the frequency of the transition from the upper level of a forbidden transition to the next upper state, the line shift for the absorption at dipole-forbidden transition can reach a large magnitude. The possibility of radiation amplification without population inversion at dipole-forbidden and quasi-resonant transitions is predicted for sufficiently high intensities and small frequency detuning from the eigenfrequency of quasi-resonant transition.