Similarity criteria related to heat conduction and diffusion (Prandtl and Schmidt numbers) are studied in strongly non-equilibrium reacting flows on the basis of the Chapman–Enskog method. A one-temperature flow description is applied to study high-temperature gas mixtures with slow chemical reactions and excited rovibrational and electronic degrees of freedom of molecules and electronic states of atomic species. Essentially non-monotonic dependence of the Prandtl number on the mixture composition is emphasized; the Schmidt numbers vary weakly with temperature and decrease monotonically with increasing molecular molar fraction. For vibrationally non-equilibrium flows, we consider the detailed state-to-state model. In this case the Prandtl number is determined by translational and rotational energies; the Schmidt numbers are introduced for each vibrational state. The developed models are used to study Prandtl and Schmidt numbers in shock heated and supersonic expanding flows of N2/N and O2/O mixtures. Peculiar