The theory of nutation N.M.R. for a quadrupolar nucleus with spin quantumI= 5/2 is presented in an exact, analytical 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 calculated from the eigenvalues of a 6th-degree secular equation that is reduced to 2 secular equations of order 3. This reduction is obtained by a transformation of bases. An extension of the nutation experiment,xx¯-nutation, is compared with the standard technique. The theoretical spectra are compared with experimental27Al spectra of NH4Al(SO4)2· 12H2O and zeolite NaA.