In experiments on S-L heteronuclear spin systems with evolution of the S-spin magnetization under the influence of a quadrupolar nucleus (L-spin), effects of longitudinal quadrupolar (T-1Q) relaxation of the L-spin coherence on the sub-millisecond time scale have been documented and explored, and methods for minimizing their effect have been demonstrated. The longitudinal relaxation results in heteronuclear dephasing even in the reference signal S-0 of S{L} REDOR, REAPDOR, RIDER, or SPIDER experiments, due to T-1Q-relaxation of the transiently generated SyL2 coherence, reducing or even eliminating the observable dephasing Delta S. Pulse sequences for measuring an improved reference signal S-00 with minimal heteronuclear recoupling but the same number of pulses as for So and S have been demonstrated. From the observed intensity Delta S-0 = S-00 - S-0 and the SPIDER signal AS/S-0, T-1Q can be estimated. Accelerated decays analogous to the dipolar So curves Will Occur in T-2 measurements for J-coupled S-L spin pairs. Even in the absence of recoupling pulses, fast T1Q relaxation of the unobserved nucleus shortens the transverse relaxation time T-2s.MAS of the observed nucleus, in particular at low spinning frequencies, due to unavoidable heteronuclear dipolar evolution during a rotation period. The observed spinning-frequency dependence of T-2S.MAS matches the theoretical prediction and may be used to estimate T-1Q. The effects are demonstrated on several C-13{N-14} spin systems, including an arginine derivative, the natural N-acetylated polysaccharide chitin, and a model peptide, (POG)(10). (C) 2009 Elsevier Inc. All rights reserved.