A theoretical and experimental study is made of the response of a two-ingredient spin system when repeatedly pulsed at resonance by a number of 90° rf pulses. With a long train of 90° pulses, a sustained chain of solid echoes was produced for Na23 in NaF. The peak echo amplitude was found to decay nonexponentially for short times (i.e., the first few echoes), settling down for long times to an exponential decay characterized by a time constant T2∊. A theoretical expression for T2∊ derived in a similar manner to that for a single-ingredient spin system, described previously by Waugh and Wang and by Mansfield and Ware, does not fit the experimental data. A more general theoretical approach to the multiple-pulse experiments is developed, based on the use of a logarithmic operator. Using this formalism together with a line-narrowing model similar to Anderson's theory of spectral line narrowing in solids in the presence of an exchange interaction, a new expression for T2∊ is derived. Some related long-pulse experiments have been performed in which the Na23 magnetization following an initial 90° pulse is spin-locked in a low rf field. These experiments simulate the mean rf field in the multiple-pulse experiment. Oscillation of the spin-locked magnetization is observed. Theoretical expressions are derived which describe these oscillations, and their relation to the multiple-pulse experiments is discussed. Mentioned briefly are some multiple-pulse experiments on F19 in CaF2 doped with paramagnetic impurities; also discussed briefly are some earlier multiple-pulse double-resonance experiments carried out on both nuclear species in NaF.