A simple method to study diffusion with the help of NMR has been suggested, based on the measurement of the rate of establishment of equilibrium in a sample with initial non-equilibrium distribution of labelled species. The distribution of components in the sample during the process of diffusion was determined with the use of a standard NMR spectrometer or relaxometer. Diffusion coefficients, D, measured in water and the plastic phase of sulfolane agreed well with the data obtained by other methods. D values for dioxane in cross-linked polyurethane and for water in the lamellar phase of water-ammonium perfluorononanoate (APFN) mixtures were also measured, to demonstrate the application of the method. The technique, being a tracer method, can be applied in a number of cases where the application of spin-echo is difficult (e.g. low concentration of solvent in polymers, in conditions of incomplete averaging of internal fields, large chemical shifts etc.); for the study of mutual diffusion and dissolution kinetics of complex phase mixtures; and for the measurement of D in systems with physical hindrances to diffusion where the method allows one to determine D corresponding to 'infinite' time of observation.