This article presents gas kinetic calculation methods for the energy transport in hydrogen/ air and methane/air mixtures. The total molecular heat conductivity as well as its various shares are calculated and discussed for a temperature range of 400 to 3500 K and for a pressure of 10(5) Pa. The variation of the air/fuel ratio under the conditions of chemical equilibrium is also investigated. As opposed to our previous article, an extension of the Chapman-Enskog method which goes beyond the classical Ist approximation for elastic collisions is applied for the evaluation of suitable calculation methods. This is carried out following the method for strong relaxing thermal nonequilibrium according to Brun. The equations applied in this work are simplified formulations for the proximity to equilibrium. The method for the evaluation of the parameters of the inelastic collision and some chosen results are presented. A discussion of the various shares of the molecular heat conductivity emphasizes the considerable influence of the diffusion and the thermal diffusion processes in fuel/air mixtures compared to the Fourier heat conductivity.