  We present a theory of carrier-induced ferromagnetism in diluted magnetic
semiconductors (III_{1-x} Mn_x V) which allows for arbitrary itinerant-carrier
spin polarization and dynamic correlations. Both ingredients are essential in
identifying the system's elementary excitations and describing their
properties. We find a branch of collective modes, in addition to the spin waves
and Stoner continuum which occur in metallic ferromagnets, and predict that the
low-temperature spin stiffness is independent of the strength of the exchange
coupling between magnetic ions and itinerant carriers. We discuss the
temperature dependence of the magnetization and the heat capacity.
