  Using group theory and Kane-like $\mathbf{k\cdot p}$ model together with the
L\"owdining partition method, we derive the expressions of spin-orbit coupling
of electrons and holes, including the linear-$k$ Rashba term due to the
intrinsic structure inversion asymmetry and the cubic-$k$ Dresselhaus term due
to the bulk inversion asymmetry in wurtzite semiconductors. The coefficients of
the electron and hole Dresselhaus terms of ZnO and GaN in wurtzite structure
and GaN in zinc-blende structure are calculated using the nearest-neighbor
$sp^3$ and $sp^3s^\ast$ tight-binding models separately.
