  We give a necessary and sufficient condition for gluings of hyperconvex
metric spaces along weakly externally hyperconvex subsets in order that the
resulting space be hyperconvex. This leads to a full characterization of
gluings of two isometric copies of the same hyperconvex space. Furthermore, we
investigate the case of gluings of finite dimensional hyperconvex linear spaces
along linear subspaces. For this purpose, we characterize the convex polyhedra
in $l_\infty^n$ which are weakly externally hyperconvex.
