  We define and prove the existence of unique solutions of an asymptotic
Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space
of signature (2, n): the boundary data is given by loops on the boundary at
infinity of the pseudo-hyperbolic space which are limits of positive curves. We
also discuss a compact Plateau problem. The required compactness arguments rely
on an analysis of the pseudo-holomorphic curves defined by the Gauss lifts of
the maximal surfaces.
