Above a certain Mach number, several aerodynamic properties become asymptotically independent of the free stream Mach number, such as pressure coefficient, lift and wave-drag coefficients, and flow-field structure. Known as Mach number independence principle, this phenomenon is important for hypersonic flow analysis and hypersonic vehicle designs. Proceeding from the contents of Mach number independence principle, we numerically study the applicability of the law in thermo-chemical nonequilibrium flow by applying Navier-Stokes equation in a five-component system. Sphere-cylinder is chosen as simulation model with radius 5cm considering the double scale law and the free-stream is at H=60km. To study the effects of nonequilibrium flow, we compare it with frozen flow and thermal equilibrium flow. The flows are set as viscous or inviscid. For viscous flow, the wall boundaries are treated by assuming an adiabatic or isothermal wall for laminar flow. Wave-drag, lift and friction coefficient, boundary layer distribution, shock shapes and pressure distribution along the wall are given for several combinations of Mach number and gas states (frozen, thermal equilibrium and thermo-chemical nonequilibrium gas). For sphere-cylinder bodies considered here, Mach number independence principle only exists for wave-drag coefficient in the considering nonequilibrium flow due to the coupled effects of real-gas and expansion.