General expressions for the translational and vibrational contributions, λ T T , λ T T , λ T T and λ T T , to the thermal conductivities of dilute molecular gases are presented. Numerical results are achieved by combining: approximations to deal with inelastic collisions; correlations for the reduced collision integrals Ω(2,2)∗ and Ω(1,1)∗ based on the principle of corresponding states; and experimental data on vibrational relaxation. Illustrative calculations are given for N 2 and I 2 gases for both equilibrium and non-equilibrium cases. They show that effects of vibratrional-translated non-equilibrium on thermal conductivity may be substantial and important.