The optical reflectivity method was used to investigate the structure of shock fronts in argon from Mach 1.70 to Mach 4.85 and in nitrogen from Mach 2.01 to Mach 3.72. Experimental data were obtained at two wavelengths and over a wide range of initial pressures. The reflectivities, corrected empirically for shock curvature, were fitted to a bimodal profile to yield a maximum‐slope density thickness. The reciprocal of the thickness in argon (expressed in terms of the Maxwellian mean free path in the undisturbed gas) rises rapidly to a maximum of approximately 0.31 at about Mach 3.5 and decreases gradually thereafter. Above Mach 3 the thickness is about 50% greater than calculated from the Navier‐Stokes equations, using a realistic viscosity‐temperature relationship. There is excellent agreement, especially at the higher shock strengths, with recent bimodal calculations carried out by Muckenfuss, using realistic intermolecular potentials. In nitrogen, the shocks are thinner than in argon and appear to attain a minimum value of 2.5 initial mean free paths at about Mach 3.7. Rotational relaxation appears to be as rapid in the strong shocks as previously observed in weak shocks; it appears to be completed within the shock front. The experimental density thicknesses are approximately 50% greater than those calculated from the Navier‐Stokes equations, using the experimental shear viscosity &mgr; and a bulk viscosity of 2&mgr;/3. The agreement with these Navier‐Stokes solutions is about as good as those in argon.