  We calculate the off-diagonal long range order (ODLRO) terms of the
exciton--exciton correlation function of a semiconductor bilayer system with
Coulomb interaction and a transverse magnetic field. We show that the formation
of a BEC state is very sensitive to the width of the interaction in momentum
space. This dependence is analytically derived and represents the key physical
ingredient for the formation (or not) of an exciton condensate state.
