Physical-chemical processes in a shock layer past a slender spherically blunted body at high supersonic velocities are investigated. Using a gas-dynamic model, defined by the complete viscous shock-layer equations , the steady laminar axisymmetric flow of viscous, heat-conducting, partially dissociated and ionized air under chemical and thermal non-equilibrium is considered throughout the region between the body and the required thin shock wave. Attention is concentrated on the non-equilibrium chemical, ionization, and relaxation kinetics at large distances from the leading stagnation point. Multicomponent diffusion and the reverse influence of dissociation-recombination on the relaxation of vibrational quantum states, i.e. coupling vibration-dissociation-vibration (CVDV), are taken into account. A new model is used to describe dissociation-relaxation process . The model includes the effect of non-equilibrium excitation of vibrations and the equilibrium excitation of rotational molecular modes on the dissociation rate constants. Comparisons with experimentally verified calculations and calculations within the scope of the chemically equilibrium full viscous shock-layer model indicate that the model is physically adequate. The calculations highlighted physical effects in the non-equilibrium viscous shock layer past a slender spherically blunted cone at various distances from the stagnation point.