  We propose and analyze a modified ghost-interference experiment, and show
that revealing the particle-nature of a particle passing through a double-slit
hides the wave-nature of a spatially separated particle which it is entangled
with. We derive a nonlocal duality relation, ${\mathcal D}_1^2 + {\mathcal
V}_2^2 \le 1$, which connects the path distinguishability of one particle to
the interference visibility of the other. It extends Bohr's principle of
complementarity to a nonlocal scenario. We also propose a ghost quantum eraser
in which, erasing the which-path information of one particle brings back the
interference fringes of the other.
