This is a theoretical study of nuclear magnetic resonance (NMR) spectra to be obtained from a powder specimen spinning in the magnetic field. The nuclear system is assumed to be magnetically dilute and to exhibit a combination of electric quadrupole interaction, magnetic shielding anisotropy and heteronuclear spin coupling. Formulas are given for the line positions and centreband linewidths of all transitions of the quadrupolar nucleus, in terms of scalar products of local interaction tensors. A number of unusual effects are predicted.