Three methods are described for the generation of alternating voltages having a square‐wave shape and covering a wide range of frequencies. The first method is based on a previously developed system and uses an overloaded direct‐coupled degenerative vacuum‐tube amplifier. The second method uses a special pulse generator followed by a vacuum‐tube trigger circuit. The third method is a combination of the first two and produces waves which are squarer than those produced by the individual systems. Very square waves are obtained with all systems at frequencies up to 200 kilocycles per second and with loading capacities up to 100 micromicrofarads. The applications of these waves are considered, as well as the importance of the circuits for other purposes. Of special interest are the suggested improvements in conventional ``scale‐of‐two'' counting circuits and the description of the high frequency pulsing circuit.