Relaxation processes induced by the antisymmetric part of the chemical shift anisotropy tensor ͑henceforth called anti-CSA͒ are usually neglected in NMR relaxation studies. It is shown here that anti-CSA components contribute to longitudinal relaxation rates of the indole 15 N 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 15 N, the 15 N-1 H dipole-dipole ͑DD͒ cross-relaxation rates ͑Overhauser effects͒, and the cross-correlated CSA/DD relaxation rates involving the second-rank symmetric part of the CSA tensor of 15 N at four magnetic fields B 0 = 9.4, 14.1, 18.8, and 22.3 T ͑400, 600, 800, and 950 MHz for protons͒ over a temperature range of 270Ͻ T Ͻ 310 K. A good agreement between experimental and theoretical rates can only be obtained if the CSA tensor is assumed to comprise first-rank antisymmetric ͑anti-CSA͒ components. The magnitude of the hitherto neglected antisymmetric components is of the order of 10% of the CSA.