Abstract 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 Spectral method of Streett , Zang, and Hussaini. The high enthalpy hypersonic flows around a circumference, around a reentry capsule, along a blunt body, and along a double ellipse in two-dimensions are simulated. The Van Leer, Liou and Steffen Jr., and Steger and Warming flux vector split ting algorithms are applied to execute the numerical experiments. Three temperatures, which are the translational-rotational temperature, the vibrational temperature, and the electron temperature, are used to accomplish the numerical comparisons. Excellent results were obtained with minimum errors inferior to 6.0%. The key contribution of this work is the correct implementation of a three temperature model coupled with the implementation of three algorithms to perform the numerical simulations, as well the description of energy exchange mechanisms to perform more realistic simulations.