The results of the theoretical investigation of the semiconductor susceptibilities in the frame of pump–probe approach in the nonstationary regime are presented using the exciton–photon and elastic exciton–exciton interactions . We suppose that the powerful time-varying pump pulse excites excitons. These excitons interact with each other and the weak laser pulse with the frequency tuned to the exciton transition tests the optical properties of a semiconductor. We obtained differential equations describing behavior of the concentration of excitons, dispersive and absorptive components of the susceptibility in the non-stationary regime, which depend on the detunings of the test and pump pulses and on the intensity of pump pulse. We obtained the results describing dependences of concentration excitons in time and intensity of radiation, which depend on the detunings of pump pulses in the case when the pump pulse has a rectangular and Gauss form. We predict the oscillatory regime at small times, the intensity of which increases with the increase of the amplitude a pump pulse. Dependences of concentration of excitons change jump-like at large intensity and detuning of the pump pulse. At switching-off of an pump pulse concentration of excitons decreases exponentially. Incident on the semiconductor Gauss pulse behavior of the exciton concentration observed oscillatory regime at the forefront of the pump pulse. We also obtained results describing dependence absorptive components of susceptibility on time and intensity of radiation, which depend on the detuning of pump pulse too. Their behavior also is characterized by presence of an oscillatory regime at small times. This oscillatory regime leads to occurrence of negative values in absorptive components of susceptibility that evidences about the strengthening of a test pulse. Resonant values of radiation intensity of a pump pulse show the strong oscillatory regime in behavior of optical functions. Parametric resonance is most pronounced when the pump pulse has a stepped appearance. It was found that the resonant oscillation regime is observed then time dependence of the exciton density is steady state. This allowed us to reduce the number of differential equations and find resonance values for the parameters. Was obtained exact solve for the system of differential equations for the quasi-stationary case. Was found the expression for the characteristic coefficient. It shows that the real and imaginary part of the characteristic coefficient strongly varies in a narrow range of the values of the intensity of the incident pulse and resonance detuning. This fact confirms the possibility of parametric resonance for given values of the pump intensity and the detuning. Changing the shape of the pump pulse significantly changes the behavior of the optical functions too. Resonance values of the pump pulse and detunings are also observed for the Gauss pulse. We also obtained results describing dependences of dispersive component of susceptibility on time and intensity of radiation, which depend on the detuning of pump pulse. It was found that at low intensities of incident radiation the dispersion law has the polariton-like form due to the excitonphoton interaction. For the normal dispersion the oscillatory regime is observed at short time. The anomal region of the dispersion law for the increase of the pump appears at the positive detunings. For negative detunings the increase of the pump field leads to the increasing of the normal region of the dispersion law. These changes the dispersion law evidences about the shifting of the absorption and gain bands with the increase of the level of excitation. We have investigated also the stability of the obtained solution.