The theory of nutation NMR of quadrupolar nuclei with half-integer spin is treated for 2 different exptl. situations. In the std. expt., x nutation, the evolution of the spins is studied when subjected to a resonant r.f. pulse of phase x. For a spin I = 3/2 the nutation of the magnetization is described by 4 sep. oscillatory time-dependent terms. These 4 nutation frequencies are detd. by transitions between the 4 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 an x, -x-nutation expt. is investigated where the spins are subjected to a sequence of 2 pulses, one with phase x and the next one with phase -x. Again, 4 nutation frequencies were found, but corresponding to different transitions in the rotating frame than in the x nutation expt. The calcd. nutation spectra for both situations are compared with exptl. spectra of NaNO3.