The propagation of high-velocity shock waves in an axial maganetic field generated by single-turn coils connected in parallel to a condenser bank is investigated. Time-resolved photographs show that the plasma behind the shock front is driven away from the tube walls by the maganetic pressure, This compression heats the ionized gas and maintains a high shock velocity during the transit of the front through the coil. The compressed plasma appears to be stable and undergoes radial oscillations that follow the current oscillations. The interpretation and significance of these observations in controlled thermounclear fusion research are discussed. (auth)