A steady laminar axisymmetric flow of viscous, heat conducting, nonequilibrium, partially dissociated, and ionized air past a thin slender sphere-cone is considered. The flowfield characteristics with the interplay between reactions and vibrational relaxation taken into account are investigated. An "adiabatic" dissociation model accounting for both nonequilibrium excitation of vibrational modes and equilibrium excitation of rotational modes of the air molecules is used to calculate thermal nonequilibrium dissociation rate constants. In the case of thermal equilibrium, the model yields a good agreement of dissociation constants with experimental data widely used in hypersonic calculations. The combined effect of the multicomponent diffusion with real binary diffusion coefficients on the heat transfer rates has been evaluated. Quantitative assessments of the influence of thermal nonequilibrium on the flow parameters have been obtained at various freestream conditions. The influence of the body surface activity with respect to accommodation of vibrational energy on the heat transfer rate has been evaluated.