M Moser, A Prets and W L Spitzer Time Evolution of Spin Waves (20K, Rev-Tex) ABSTRACT. A rigorous derivation of macroscopic spin-wave equations is demonstrated. We introduce a macroscopic mean-field limit and derive the so-called Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic Heisenberg model at $T=0$ and finally extend our analysis to general spin hamiltonians for the same class of ferromagnetic ground states.