  Bilayer electron-hole systems with unequal electron and hole densities are
expected to have exciton condensate ground states with spontaneous
spin-polarization in both conduction and valence bands. In the absence of
spin-orbit and electron-hole exchange interactions there is no coupling between
the spin-orientations in the two quantum wells. In this article we show that
Rashba spin-orbit interactions lead to unconventional magnetic anisotropies,
whose strength we estimate, and to ordered states with unusual quasiparticle
spectra.
