The two‐dimensional steady‐state reaction‐zone structure of a homogeneous and a heterogeneous explosive is studied. To do this theoretical results obtained from the Euler equations of compressible flow are combined with experimental data on steady‐state detonation shock‐wave speed and shape as a function of the explosive charge size. The theoretical results, constrained by the experiments, define an inverse problem for the chemical heat‐release function in the reaction zone which follows the shock wave; this problem is solved. The heterogeneous explosive is made from the homogeneous one by adding small quantities of other materials. Because of this, the two explosives were closely related in many respects. In spite of this, quite large differences in the detonation characteristics are observed between the two explosives, both in the wave speed as a function of charge size and in the shape of shock‐wave loci near the explosive edge. It is found that a single forward rate exponentially dependent on the inverse of the local shock pressure can ‘‘explain’’ the homogeneous case observations, but that a rate with much less state dependence near the explosive edge is necessary to understand the observations for the heterogeneous material. Near the failure diameter of both materials, prominent structures are found on the experimental shock‐wave loci. These structures would seem to be incompatible with a steady flow and call into question whether two‐dimensional steady‐state detonations occur at all in condensed explosives near their failure diameter.