Asymmetries in the manifold of spinning sidebands (ssbs) from the satellite transitions have been observed in variable-temperature Al-27 MAS NMR spectra of alum (KAl(SO4)(2)(.)12H(2)O), recorded in the temperature range from -76 to 92 degrees C. The asymmetries decrease with increasing temperature and reflect the fact that the ssbs exhibit systematically different linewidths for different spectral regions of the manifold. From spin-echo Al-27 NMR experiments on a single-crystal of alum, it is demonstrated that these variations in linewidth originate from differences in transverse (T-2) relaxation times for the two inner (m = 1/2 -> m = 3/2 and m = -1/2 <-> m = -3/2) and correspondingly for the two outer (m = 3/2 <-> m = 5/2 and m = -3/2 <-> m = -5/2) satellite transitions. T, relaxation times in the range 0.5-3.5 ms are observed for the individual satellite transitions at -50 degrees C and 7.05 T, whereas the corresponding T, relaxation times, determined from similar sa tu ration-recovery 27Al NMR experiments, are almost constant (T-1 = 0.07-0.10 s) for the individual satellite transitions. The variation in T-2 values for the individual Al-27 satellite transitions for alum is justified by a simple theoretical approach which considers the cross-correlation of the local fluctuating fields from the quadrupolar coupling and the heteronuclear (Al-27-H-1) dipolar interaction on the T-2 relaxation times for the individual transitions. This approach and the observed differences in T-2 values indicate that a single random motional process modulates both the quadrupolar and heteronuclear dipolar interactions for Al-27 in alum at low temperatures. (c) 2004 Elsevier Inc. All rights reserved.