The nature of the transfer, within a single nuclear spin system, of energy absorbed from an external source of radio-frequency magnetic field has been investigated by a double-irradiation technique. Energy from a high-power oscillator running at fixed frequency is absorbed by the nuclear spin system. The frequency of a second, low-level oscillator is then swept through the nuclear resonance, sampling the line shape existing in the presence of the strong rf field from the fixed-frequency oscillator. Particular spin systems investigated were the proton system in single crystalline CaSO4.2H2O, and the Al27 system in aluminum metal. In aluminum, the technique gives direct experimental verification of a completely homogeneous saturation behavior, a behavior expected from elementary considerations. It also gives further verification of the Redfield saturation theory. In CaSO4.2H2O, an enhancement effect is observed which allows one to determine the importance of double-flip spin-lattice relaxation processes. The technique could be usefully applied to many spin systems to determine the degree of inhomogeneity in the resonance line broadening.