A numerical investigation of unsteady hypersonic shock/shock interference flows classified by Edney (Edney, B. E., 'Anomalous Heat Transfer and Pressure Distributions on Blunt Bodies at Hypersonic Speeds in the Presence of an Impinging Shock,' Aeronautical Research Inst. of Sweden, FFA Rept. 115, Stockholm, Sweden, Feb. 1968) considering the thermochemical nonequilibrium effect is presented. The numerical method used is composed of the fourth-order compact MUSCL total variational diminishing scheme, the maximum second-order lower-upper symmetric Gauss-Seidel scheme, and the advection upstream splitting method scheme for capturing shocks and vortices accurately. The two-temperature model based on the Park model (Park, C., 'Two-Temperature Interpretation of Dissociation Rate Data for N2 and O2,' AIAA Paper 88-0458, Jan. 1988) has taken the thermochemical nonequilibrium into consideration. The nitrogen flows under several flow conditions are calculated. The obtained results show that the type of the shock/shock interference is strongly dependent on the location of the impinging shock as well as the shock standoff distance. Finally, unsteady flow characteristics associated with the thermochemical nonequilibrium effect, especially very complicated flow structures involving shocks, compression waves, vortices, and their interactions, are investigated and explained.