We present a theoretical description and computer simulations for the overtone NMR of half-integer quadrupolar nuclei in solids. It is shown that the overtone NMR has the ability to produce high-resolution solid NMR spectra for the quadrupolar nuclei under magic angle spinning conditions. We demonstrate that when polycrystalline 23 Na2MoO4 is placed in the static magnetic field of 7.05 T, the direct detection of the overtone NMR is possible. It becomes, however, apparent that indirect detection schemes are required to obtain the usual NMR spectra that have separated resonance lines corresponding to chemically non-equivalent sites. (c) 2005 Elsevier B.V. All rights reserved.