In a method for the simultaneous measurement of spin resonance signals, in particular NMR signals, from layers located at different depths in a test volume, simultaneous excitation of the different layers is effected by a multiple-component rf excitation pulse P.sub.n, consisting of n individual components P.sub.m with the frequencies .omega..sub.m, which act selectively on defined layers m of the test volume, in the presence of a layer-selective gradient, the individual components P.sub.m having a phase displacement .phi..sub.m which is varied from one sequence to the next by successive addition of a constant phase increment .DELTA..phi..sub.m modulo 360 fixed individually for each individual component P.sub.m. If phase coding is effected according to the "Fast Fourier Flow Technique" with the aid of a bipolar gradient pulse, then the flow velocity of a medium moving through the test volume can be measured directly in a multi-dimensional Fourier transformation experiment, simultaneous for several flow cross-sections, in a single recording cycle.