High-speed right-angle geared rotor systems are widely used in automotive and rotorcraft transmission applications. Hypoid gear pairs are one of the commonly applied right-angle geared systems. They are designed to transmit significant amount of rotational power between two perpendicular, non-intersecting shafts. However, this class of geared rotor systems is often plagued by excessive vibration and noise problems. In most cases, the gear whine generated leads to costly warranty issues. This thesis work is focused on the dynamic response analysis of a generic hypoid gear pair. A unique non-linear timevarying dynamic model of the hypoid gear pair system is proposed which includes backlash non-linearity, linear time-varying gear meshing stiffness, time-varying mesh characteristic vectors as well as sliding friction effects. The model is applied to study the physical phenomenon governing the generation of dynamic mesh force that is believed to be the main cause of high vibration and noise levels. Solutions are presented in the forms of semi-analytical and numerical integration results. Parametric studies reveal new, previously unstudied findings of the controlling factors and vibratory behaviors under light, medium, and high mean loads. Using the numerical simulation, critical non-linear behaviors in system response such as the jump phenomenon, impact regimes, subharmonic, and chaotic resonance are investigated. Classification of the steady-state solutions is presented based on the results of time histories, phase plane plots, Poincare maps, and Fourier spectra.