  We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$
components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of
the solution at time $t\in\R$. The initial measure $\mu_0$ has a
translation-invariant correlation matrix, zero mean, and finite mean energy
density. It also satisfies a Rosenblatt- resp. Ibragimov-Linnik type mixing
condition. The main result is the convergence of $\mu_t$ to a Gaussian measure
as $t\to\infty$. The proof is based on the long time asymptotics of the Green's
function and on Bernstein's ``room-corridors'' method.
