The unified model was proposed for the three configurations of the composite motion of curve-face gear pair. A coupled bending-torsional-axial dynamic model with multi degree-of-freedom transmission system was proposed comprehensively considering nonlinear parameters such as tooth mesh stiffness, static transmission error and backlash. The fourth-order Runge–Kutta numerical method was applied to solve the dimensionless dynamic differential equations of the system, and then the dynamic responses of the system were investigated by time history, phase-plane portrait, poincare map, FFT spectrum and bifurcation diagram. It was found that the dynamic responses of the three configurations were complex. It presented quasi-periodic motion only under certain configuration and parameter conditions. With the increase of meshing frequency, the system state was characterized by the alternation between chaotic motion and periodic motion. Eccentricity ratio of displacement curve of curve-face gear pair mainly affected the rotational frequency of the system. As the eccentricity ratio increased, the dominant frequency of the system gradually changed from meshing frequency to rotational frequency. The correctness of the theoretical model was verified through corresponding experimental studies.