  In this paper, we study the change of the ADM mass of an ALE space along the
Ricci flow. Thus we first show that the ALE property is preserved under the
Ricci flow. Then, we show that the mass is invariant under the flow in
dimension three (similar results hold in higher dimension with more
assumptions). A consequence of this result is the following. Let $(M,g)$ be an
ALE manifold of dimension $n=3$. If $m(g)\neq 0$, then the Ricci flow starting
at $g$ can not have Euclidean space as its (uniform) limit.
