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The theory of nutation NMR of quadrupolar nuclei with half-integer spin is treated for two different experimental situations. In the standard experiment, x nutation, the evolution of the spins is studied when subjected to a resonant r.f. pulse of phase x. It is shown that for a spin I= 3/2 the nutation of the magnetization is described by four separate oscillatory time-dependent terms. These four nutation frequencies are determined by transitions between the four eigenstates of the spin in the rotating frame. The nutation spectrum in many cases gives much more information than a normal NMR spectrum of the same nucleus. Unfortunately, however, the nutation spectrum is sometimes too complicated to interpret. Therefore a x, –x-nutation experiment is investigated where the spins are subjected to a sequence of two pulses, one with phase x and the next one with phase –x. Again four nutation frequencies are found, but corresponding to different transitions in the rotating frame than in the x nutation experiment. The calculated nutation spectra for both situations are compared with experimental spectra of NaNO3.