A hydrodynamic theory of spin waves is developed for certain magnetic systems in analogy with the derivation of two-fluid hydrodynamics for liquid helium. The systems considered are "isotropic" and "planar" ferromagnets and antiferromagnets. In each system, low-frequency spin waves are predicted to exist at long wavelengths for any temperature below the transition to the paramagnetic phase. The real part of the frequency is given exactly in terms of thermodynamic quantities. The damping rate is