At very low or low frequency, the so-called dispersion curves (longitudinal relaxation rate as a function of the measurement frequency) are obtained with a ''relaxometer,'' which is generally run according to the ''field-cycling'' technique. Because of the very poor field homogeneity, relaxation times of a single (broad) signal are measured. When going to higher fields, with standard nuclear magnetic resonance spectrometers (possibly with variable field capacities), different lines are resolved. We show how the relaxation rates pertaining to these lines can be connected to the results obtained via the relaxometer. Among other things, we demonstrate why the magnitude mode (generally used for processing the relaxometer data) must be used with caution when several lines are resolved. Actually, we could obtain accurate 1 H dispersion curves in a very broad frequency range (5 kHz-400 MHz), and we show that a decomposition into several Lorentzian curves proves to be adequate, as far as paramagnetic relaxation due to dissolved oxygen is concerned. The method will be applied i) to nondegassed liquid toluene, ii) to the same solvent involved in the formation of an organogel. In that latter case, a low frequency contribution to the dispersion curve (possibly non-Lorentzian) reveals the part of the solvent within the organogel structure. The algorithm used for analyzing these dispersion curves is described.