Different vibrational nonequilibrium processes are reviewed as well as the corresponding zeroth-order distribution functions and relaxation equations. Two methods for the calculation of transport coefficients are then presented. The first is based on the expansion of the first order distribution function in orthogonal polynomials thus, model equations and consequently rotational and vibrational relaxation equations can be found. In the pressure tensor, diagonal terms of relaxation pressure appear and the results of a numerical calculation of these terms are given for the case of a rapidly expanding nitrogen flow. The second method consists of using a generalized Bhatnagar–Gross–Krook–Morse method from which simpler but more tractable results are obtained.