The hypersonic (M=25) flow past a 10° right circular cone at 0° angle of attack has been computed using an implicit, noniterative, finite-difference scheme for the Parabolized Navier-Stokes (PNS) equations. Three different gas models have been considered in the study — (1) ideal gas (γ = constant), (2) equilibrium air, and (3) five species (N2, O2, NO, N, O) chemical nonequilibrium air. For the nonequilibrium air case, three different models have been considered — (a) one in which the constituent species have no internal structure (i.e., species are ideal gases), (b) one in which the constituent species have internal structure (i.e., species are thermally perfect gases), and (c) one in which the species have internal structure and their thermodynamic properties have been obtained from quantum mechanical and spectroscopic calculations.