Two-dimensional supersonic flows with heat addition from given internal sources and/or nonequilibrium condensation are considered. The critical amount of heat necessary to thermally choke the flow is de??ned at any point in the flow ??eld, and the necessary and su??cient conditions for thermal choking are identi??ed from the singularities of the equations of motion along streamlines. In particular, for any practical purposes, it is shown that the flow Mach number reaches unity at any point where the heat added to the flow along the streamline passing through that point reaches the critical value. Thermally choked flows are then identi??ed as those flows where the critical heat along streamlines is exceeded leading to embedded oblique shock waves with a local subsonic flow ??eld downstream.