The magnitudes and orientations of the principal elements of the H-1 chemical shift, H-1-N-15 dipolar coupling, and N-15 chemical shift interaction tensors in N-15(epsilon l)-tryptophan and N-15(pi)-histidine nitrogen sites were determined by. the analysis of three-dimensional powder patterns obtained from N-15-labeled powder samples of the amino acids. Although the magnitudes of the principal elements of the H-1 and N-15 chemical shift tensors for these two sites are quite different, their molecular orientations in the molecular frame are very similar. The least shielded N-15 chemical shift tensor element, sigma(33N), and the most shielded H-1 chemical shift tensor element, sigma(11H), are approximately colinear with the N-H bond in both cases. The principal elements, sigma(22H) and sigma(22N), are in the plane of the indole ring for tryptophan and in the plane of the imidazole ring for histidine but oppose each other. sigma(11N) and sigma(33H) are perpendicular to the planes of these heterocyclic rings, The chemical shift tensors of the H-1 and N-15 nuclei in these two side chain nitrogen sites are distinctly different from those of backbone amide nitrogen sites.