Summary: The reflection of asymmetric shock waves in steady flows is studied both theoretically and experimentally. While the analytical model was two-dimensional, three-dimensional edge effects influenced the experiments. In addition to regular and Mach reflection wave configurations, an inverse-Mach reflection wave configuration, which has been observed so far only in unsteady flows (e.g. shock wave reflection over concave surfaces or over double wedges) has been recorded. A hysteresis phenomenon, similar to the one that exists in the reflection of symmetric shock waves, has been also found to exist in the reflection of asymmetric shock waves. The domains and transition boundaries of the various types of overall reflection wave configurations are predicted analytically.