Stress tensor in viscous chemically non-equilibrium N2/N flows with electronic excitation is studied. A one-temperature model of a flow with slow dissociation reaction taking into account translational, rotational, vibrational degrees of freedom as well as electronic states of both molecules and atoms is developed. The generalized Chapman–Enskog method is used to derive the closed set of governing equations and to evaluate the normal mean stress. The bulk viscosity and relaxation pressure are calculated in the temperature range 2000–10000 K for various mixture compositions. Various models for the dissociation cross section are used to calculate the relaxation pressure. The influence of mixture composition and electronic excitation on the normal mean stress is discussed.