Relaxation processes induced by the antisymmetric part of the chemical shift anisotropy tensor (henceforth called anti-CSA) are usually neglected in NMR relaxation studies. It is shown here that anti-CSA components contribute to longitudinal relaxation rates of the indole N-15 nucleus in tryptophan in solution at different magnetic fields and temperatures. To determine the parameters of several models for rotational diffusion and internal dynamics, we measured the longitudinal relaxation rates R-1=1/T-1 of N-15, the N-15-H-1 dipole-dipole (DD) cross-relaxation rates (Overhauser effects), and the cross-correlated CSA/DD relaxation rates involving the second-rank symmetric part of the CSA tensor of N-15 at four magnetic fields B-0=9.4, 14.1, 18.8, and 22.3 T (400, 600, 800, and 950 MHz for protons) over a temperature range of 270