Endothermic and exothermic processes in gas dynamic flows taking place in a very narrow zone may be considered as discontinuities. The variation of the static and total head density ratio, pressure ratio, and temperature ratio as well as the angle of deviation, area ratio, and exit normal Mach number have been found as functions of the entry normal Mach number and of heat addition. In addition to these, some other useful quantities such as the area ratio parameter, the difference of the square of velocities, and the normal velocity product have been evaluated. It was found that, in a discontinuity, heat can be added until the exit normal Mach number reaches unity (choking). Depending on the entry normal Mach number, only a limited amount of heat can be added at the discontinuity. An exothermic discontinuity behaves as an expansion when the entry normal Mach number is subsonic, and it is accompanied by a drop in static pressure, density, and total head pressure. An exothermic discontinuity behaves as a compression shock wave when the entry normal Mach number is supersonic, and it is accompanied by an increase in static pressure and density and a decrease in total head pressure. An endothermic discontinuity behaves always as a compression shock wave, and it is accompanied by an increase in static density, pressure, and total head pressure. It is hoped that the results and conclusions found may be useful in a better understanding of many nearly discontinuous phenomena such as flame fronts, condensation and evaporation fronts, and other similar problems.