  In this paper we solve the Plateau problem for spacelike surfaces with
constant mean curvature in Lorentz-Minkowski three-space $\l^3$ and spanning
two circular (axially symmetric) contours in parallel planes. We prove that
rotational symmetric surfaces are the only compact spacelike surfaces in $\l^3$
of constant mean curvature bounded by two concentric circles in parallel
planes. As conclusion, we characterize spacelike surfaces of revolution with
constant mean curvature as the only that either i) are the solutions of the
exterior Dirichlet problem for constant boundary data or ii) have an isolated
conical-type singularity.
