We have investigated the effects of the spin-orbit interaction on the valence-band structure of wurtzite GaN in the k∙p theory. The spin-orbit interaction is usually neglected in nitrides, which leads to three doubly degenerate bands: the heavy-hole, light-hole, and crystal-field split-off bands. Including the spin-orbit interaction, this degeneracy is removed to give six single bands. We obtained the Luttinger-like parameters in bulk wurtzite GaN by fitting data obtained from an empirical pseudopotential calculation obtaining a value for the parameter A7 of 93.7 meV/Å. We also used these results to calculate the valence-band structures of a GaN/AlGaN quantum well. Our result shows the spin-orbit interaction is important in GaN and associated quantum well structures. © 1999 American Institute of Physics.