<p>Non-circular beveloid gears (NBGs) combine the prescribed variable transmission ratio of non-circular gears with the axial tooth-thickness variation of beveloid gears, resulting in spatial meshing and nonlinear vibration characteristics that differ from those of ordinary non-circular spur gears and conventional beveloid gears. To clarify these characteristics, this paper investigates the nonlinear vibration response of an NBG transmission system under coupled multi-parameter excitation. First, the tooth-surface equations of the NBG are derived through coordinate transformation, and a three-dimensional solid model is established. Then, time-varying meshing stiffness obtained from finite-element contact analysis, variable transmission ratio, time-dependent backlash, meshing damping and transmission error are introduced into an eight-degree-of-freedom translation-torsion nonlinear dynamic model. The governing equations are solved numerically, and bifurcation diagrams, maximum Lyapunov exponents, three-dimensional phase portraits and Poincare sections are used to identify periodic, multi-periodic, quasi-periodic and chaotic responses under variations in excitation frequency, excitation amplitude, damping and stiffness. Unlike previous studies that mainly focus on geometric modelling or single-excitation dynamics of non-circular gears, this study emphasizes the coupled influence of NBG-specific spatial geometry and multiple internal excitations on nonlinear vibration. Experimental results obtained from an NBG transmission platform show the same response trends as the numerical prediction, providing trend-level validation of the proposed model. The results provide theoretical guidance for parameter selection, vibration suppression and dynamic design of NBG transmission systems.</p>