We investigated polarization-dependent quantum beats of excitons with light and heavy holes observed in the pump-probe experiment. Oscillations in the energy of exciton resonances have been experimentally observed upon  simultaneous excitation of exciton levels. To explain this effect, a theoretical model was formulated based on the consideration of a five-level scheme with the inclusion of nonlinearity in the form of an exchange exciton-exciton  interaction. It has been found that the shift of energy resonances can be described only if the exciton-exciton exchange interaction is taken into account. The results of theoretical calculations of the coherent dynamics of excitons in this model are in agreement with the experimental data.