At shock Mach numbers Ms ∼ 16 in pure argon with initial pressures p0 ∼ 5 torr and final electron number densities ne ∼ 1017 cm−3, the translational shock front in a 10 x 18 cm hypervelocity shock tube develops sinusoidal instabilities which affect the entire shock structure including the ionization relaxation region, the electron-cascade front and the final quasi-equilibrium state. By adding a small amount of hydrogen (∼ 0·5% of the initial pressure), the entire flow is stabilized. However, the relaxation length for ionization is drastically reduced to about one-third of its pure-gas value. Using the familiar two-step collisional model coupled with radiation-energy loss and the appropriate chemical reactions, it was possible to deduce from dual-wavelength interferometric measurements a precise value for the argon-argon collisional excitation cross-section SAr Ar* = 1·0 x 10−19 cm2/eV with or without the presence of a hydrogen impurity. The reason for the success of hydrogen, and not other gases, in bringing about stabilized shock waves is not clear. It was also found that the electron-cascade front approached the translational-shock front near the shock-tube wall. This effect appears to be independent of the wall material and is not affected by the evolution of adsorbed water vapour from the walls or by water vapour added deliberately to the test gas. The sinusoidal instabilities investigated here may offer some important clues to the abatement of instabilities that lead to detonation and explosions.