The operation of transistors in the avalanche mode provides simple but effective means for generating fast pulses. With present transistors there is a large spread of avalanche voltage between individual specimens, and the paper describes a method of designing trigger circuits which require no adjustment when transistors are changed.Some selection of transistors is necessary for fast operation, and it was found that of the transistors tested, which had α cut-off frequencies in the region of 10 Mc/s, about 20% had avalanche rise times less than 10 millimicrosec, 10% less than 3 millimicrosec, and 5% less than 1.5 millimicrosec. Circuits are described for generating pulses with rise times of 1 millimicrosec and having any width from 1 millimicrosec to several microseconds at half height.The collector current of an avalanching transistor may build up to 0.5 amp in a few millimicroseconds and no suitable diodes have been found for shaping such waveforms. However, good results have been obtained by using the non-linear capacitance of diodes biased in the reverse direction.Particular attention is paid to threshold stability and the generation of pulses accurately delayed in relation to the trigger pulse.An example of a practical application of these circuits is a wide-band oscillograph described in Reference 8.