The equations for the plane viscous transonic flow of a relaxing gas are derived for free stream velocities near the equilibrium and frozen speeds of sound. One‐dimensional solutions are found which show the influence of the compressive viscosity upon the structure of a compression wave in a relaxing gas. The viscous structure of the corner region or acceleration wave which occurs when the upstream velocity just equals the frozen speed of sound is investigated in detail. The structure of a partially dispersed wave including the transition from the upstream viscous shock to the downstream relaxation zone is also determined.