The gain stability of the nuclear pulse linear amplifiers with feedback for such a fast pulse input as the step voltage or the nuclear radiation detector pulse is analysed in detail. The expression is derived which describes the waveform at the anode circuit of the photomultiplier tube which is a part of the nuclear radiation detector. It is analysed and compared when the feedback amplifier has one and two time-constants. When these fast input pulse voltages are applied to the feedback amplifier, the effects of feedback in linearity and stability of the output voltage appear only after two or three rise-times of the amplifier, And it is proved that in order to reduce this limitation, the rise time of the feedback amplifier shou1d be less than the input pulse width. It is also shown that the above theory can be applied directly to the voltage-shunt feedback amplifier stages designed as the basic amplifier of the linear amplifier, and that the gain stability is more improved for the smaller input impedance of this amplifier stage.