Abstract: This study establishes a nonlinear dynamic model and investigates the nonlinear behavior of a two-stage planetary gear transmission system. Initially, a coupled dynamic model for the dual-stage planetary gear system is constructed by considering multiple nonlinear factors including error excitation and gear backlash. Additionally, friction effects were incorporated into the analysis, where the coupled friction meshing stiffness and frictional excitation under different engagement states were systematically calculated according to diverse gear pair meshing patterns. Building upon rotational speed fluctuation considerations, numerical simulation methods were employed to systematically examine the multi-dimensional nonlinear dynamic responses under varying input speeds, encompassing temporal domain characteristics, phase space trajectories, frequency spectra, wavelet transformations, and global bifurcation features. Furthermore, practical operational conditions such as instantaneous motor startup and lubricant viscosity variations were investigated to assess their impacts on system responses. The results indicate that the transmission system exhibits significant nonlinear dynamic characteristics, showing a transition from single-period states to chaotic states as the speed changes. This reveals stable intervals and instability thresholds, where the low-speed stage has greater vibration and a wider chaotic band compared to the high-speed stage; during motor startup, the vibration is extremely large, necessitating measures to mitigate the damage caused by vibration to the system; high-viscosity lubricating oil can reduce the friction coefficient during gear meshing, decreasing energy loss and improving transmission efficiency.