  The spin density matrix for spin-3/2 hole systems can be decomposed into a
sequence of multipoles which has important higher-order contributions beyond
the ones known for electron systems [R. Winkler, Phys. Rev. B \textbf{70},
125301 (2004)]. We show here that the hole spin polarization and the
higher-order multipoles can precess due to the spin-orbit coupling in the
valence band, yet in the absence of external or effective magnetic fields. Hole
spin precession is important in the context of spin relaxation and offers the
possibility of new device applications. We discuss this precession in the
context of recent experiments and suggest a related experimental setup in which
hole spin precession gives rise to an alternating spin polarization.
