A heteronuclear double-resonance (HDR) method based on MLEV-32 or WALTZ-32 pulse sequences has been designed for the investigation of relaxation of heteronuclear multiple-quantum (MQ) coherences. The theoretical analysis of this technique uses average Hamiltonian theory (AHT) to treat the effects of coherent evolution associated with scalar couplings, offsets, and inhomogeneous radiofrequency (rf) fields during the pulse sequence. Under most conditions, the dynamics of the MQ coherences during the HDR sequence is not affected by rf inhomogeneities and scalar couplings for offsets as large as the nutation frequency. The predictions drawn from AHT are supported by numerical simulations and experiments.