The theory of nutation NMR for a quadrupolar nucleus with spin quantum I = 5/2 is presented in an exact, anal. way. It is shown that the nutation spectrum is described by 9 different frequencies each dependent on the orientation of the quadrupole tensor relative to the external field. The frequencies are calcd. from the eigenvalues of a 6th-degree secular equation that is reduced to 2 secular equations of order 3. This redn. is obtained by a transformation of bases. An extension of the nutation expt., x.hivin.x-nutation, is compared with the std. technique. The theor. spectra are compared with exptl. 27Al spectra of NH4Al(SO4)2.12H2O and zeolite NaA.