By utilizing the method of pulsed nuclear magnetic resonance, radio‐frequency energy in the form of pulses can be stored serially in a sample of nuclear spins and recalled at an arbitrary later time within the memory or relaxation time of the spin sample. Weak pulses of radio‐frequency energy condition the nuclear spins to start precessing in phase. After they become completely out of phase, a strong recollection pulse brings about a phase reversal of precession and produces a series of spin echoes in a sequence corresponding to direct or reverse order of input pulses. The echo amplitudes in such a series are given as a function of the number and strength of the input pulses and the conditions for maximum storage capacity in a spin ensemble are determined. The maximum specific storage capacity in liquids is expressed in terms of the thermal noise of the detecting apparatus, the effect of self‐diffusion of the molecules, and the relaxation times. The origin of undesired spin echoes arising from the interaction of input pulses is discussed, and means for eliminating these echoes by frequency and magnetic field modulation are discussed and applied. Extensive use is made of a magnetic field modulation technique to destroy undesired echoes, and to permit novel types of recall of serially stored groups of pulses. Whereas Fernbach and Proctor [J. Appl. Phys.26, 170 (1955)] have demonstrated multiple pulse storage under conditions which reproduce the input pulse shape, the present investigation is concerned with the storage of a maximum number of pulses whose shape is ideally determined by the nuclear spin band width. In practice, the order of 1000 rf pulses can be stored and recalled by this method in a proton sample several cc in volume within a memory time of 10 to 50 milliseconds. Large specific storage capacities expected for existing long relaxation time liquids are not realized because of excessive self‐diffusion.