In this work, a study involving the fully coupled Euler and Navier-Stokes reactive equations is performed. These equations, in conservative and finite volume contexts, employing structured spatial discretization, on a condition of thermochemical non-equilibrium, are analyzed. High-order studies are accomplished using the MUSCL procedure of Van Leer, the ENO scheme of Harten et al., the WENO scheme of Shu and the spectral method of Streett, Zang, and Hussaini. The spectral method employs collocation points and variants of Chebyshev and Legendre interpolation functions are studied. The high enthalpy hypersonic flows around a blunt body, around the VLS (Brazilian Sattelite Launcher Vehicle), around a double ellipse, around a circunference and around a reentry capsule in two-dimensions are simulated. The Van Leer, Liou Steffen Jr., and the Steger and Warming flux vector splitting algorithms are applied to execute the numerical experiments. The Euler backward integration method is employed to march the schemes in time. The reactive simulations involve Earth atmosphere chemical model of seven species and eighteen reactions, based on the Blottner model. Three temperatures, which are the translational-rotational temperature, the vibrational temperature, and the electron temperature, are used to accomplish the numerical comparisons. Results are based on qualitative and quantitative comparisons. Good results were obtained.