Larmor frequency dependent NMR studies of dipolar order relaxation in liquid crystals have seldom been tried in the past. Using conventional static magnetic field techniques, the experiment cannot be extended to the low Larmor frequency (nu(L)) regime due to limitations in the signal-to-noise ratio of the dipolar echo. In this work, we present an experimental study of the dipolar relaxation time in the frequency range 10(3)-7 x 10(7) Hz in nematic thermotropic liquid crystals. To extend the study to such low frequencies, we used the Jeener-Broekaert pulse sequence combined with fast field-cycling NMR technique. For frequencies higher than 10(5) Hz, the dipolar relaxation time T-1D(nu(L)) follows the nu(L)(1/2)-law that is characteristic of order fluctuations of the director (OFD) in nematics. In contrast, the Zeeman relaxation is driven by faster and less correlated motions, specially in the MHz frequency range. The relaxation of dipolar energy was measured to be remarkably faster than the one predicted by the usual semiclassical model of isolated spin pairs. Conceivably, the failure of the usual two-spin model should be sought in the absence of multispin interactions and multispin correlations. We propose that the OFD are the dominant relaxation mechanism for the dipolar order, even in the MHz regime. This result turns T-1D(nu(L)) experiment in a useful NMR technique for the study of slow molecular dynamics in mesophases.