In this paper, a new methodology for taking into account uncertainties based on the projection on polynomial chaos is proposed. The new approach is introduced to determine the dynamic behavior of a bevel gear system with uncertainty associated to the performance coefficient of the input aerodynamic torque.The influence of the uncertain parameters must be considered in the analysis of the dynamic response of this system. The simulation results are obtained by using the polynomial chaos approach combined with the ODE45 solver of Matlab. The proposed method is an efficient probabilistic tool for uncertainty propagation.