Three-dimensional nonequilibrium viscous hypersonic flows over ablating Teflon surfaces are studied using viscous shock-layer and parabolized Navier-Stokes (PNS) schemes. The three-dimensional nonequilibrium PNS scheme developed in this study is inherently stable in the subsonic as well as the supersonic flow regions and, thus, does not require any sublayer approximation. The scheme is formulated in terms of a general curvilinear coordinate system, and a second-order smoothing approach is used to damp the numerical solution oscillations. A new fully implicit and crossflow-coupled shock-fitting approach is used along with a pseudo-unstead y approach to significantly improve the numerical stability and computational efficiency, without compromising solution accuracy. Two test cases for the flow over a sphere-cone vehicle are considered to demonstrate this new three-dimensional nonequilibrium Teflon-air PNS scheme under zero and nonzero angle-of-attack conditions.