We consider snap-stabilization in message-passing systems. Snap-stabilization permits to design protocols that withstand transient faults: Any computation that is started after faults cease immediately satisfies the expected specification. Our contribution is twofold, as we demonstrate that in message passing systems (i) snap-stabilization is impossible for nontrivial problems if we consider channels with finite yet unbounded capacity, and (ii) snap-stabilization becomes possible in the same setting with bounded-capacity channels. The latter contribution is constructive, as we propose two snap-stabilizing protocols.