We report on the measurements of deuteron spin-spin relaxation time T-2 in the nematic phase of MBBA and 5CB using the quadrupolar echo pulse train in a magnetic field of 7 T. The spectral densities J(0)((i))(0) at different carbon sites were derived from the T-2 and T-1 measurements. Using a model that combined rotational diffusion motion of individual molecules and their internal bond rotations, the spectral densities J(1)((i))(omega(0)) and J(2)((i))(2 omega(0)) could be interpreted, while the measured J(0)((i))(0) were too large. It is argued that second-order director fluctuations contribute in part to the J(0)((i))(0) spectral densities. Thus T-2 measurements at a standard high magnetic field can be used to gain insights on director fluctuations.