Nonsecular dipolar couplings between spin-1/2 nuclei that are in close proximity to quadrupolar spins have been extensively documented in solid state nuclear magnetic resonance (NMR), particularly when involving directly bonded S = C-13, I = N-14 spin pairs. These couplings arise due to the quadrupole-induced tilting of I＇s nuclear spin quantization axes, and their most notable characteristic is that they cannot be entirely averaged away by conventional magic-angle-spinning (MAS). Nonsecular dipolar couplings can also be expected to arise when both I and S are quadrupolar nuclei, even if these have hitherto not been analyzed in detail due to the interfering effects brought about by first- and second-order quadrupolar anisotropies. Yet, the advent of new high resolution techniques for studying half-integer quadrupole nuclei in solids such as multiple-quantum MAS or dynamic-angle-spinning can change this state of affairs. The present study presents a theoretical and numerical analysis on the results that can be expected from these techniques when applied to the observation of homonuclear or heteronuclear quadrupolar spin pairs in the high field limit. Variable field multiple-quantum MAS NMR results are then presented for a variety of compounds possessing B-11- N-14, B-11- B-11 and Mn-55- Mn-55 spin pairs, that validate these theoretical predictions and illustrate the valuable information that can be extracted from analyzing these residual MAS couplings. The research potential as well as resolution limitations that according to theoretical calculations these effects will impart on MQMAS spectra recorded at low or moderate magnetic fields are thus evidenced. (C) 2000 American Institute of Physics. [S0021-9606(00)02503-4].