  The most general homogeneous monodromy conditions in $N{=}2$ string theory
are classified in terms of the conjugacy classes of the global symmetry group
$U(1,1)\otimes{\bf Z}_2$. For classes which generate a discrete subgroup $\G$,
the corresponding target space backgrounds ${\bf C}^{1,1}/\G$ include half
spaces, complex orbifolds and tori. We propose a generalization of the
intercept formula to matrix-valued twists, but find massless physical states
only for $\Gamma{=}{\bf 1}$ (untwisted) and $\Gamma{=}{\bf Z}_2$ (\`a la Mathur
and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In
particular, the sixteen ${\bf Z}_2$-twisted sectors of the $N{=}2$ string are
investigated, and the corresponding ground states are identified via
bosonization and BRST cohomology. We find enough room for an extended multiplet
of `spacetime' supersymmetry, with the number of supersymmetries being
dependent on global `spacetime' topology. However, world-sheet locality for the
chiral vertex operators does not permit interactions among all massless
`spacetime' fermions.
