  We report on small-cluster exact-diagonalization calculations which prove the
formation of electron-hole pairs (excitons) as prerequisite for spontaneous
interlayer phase coherence in bilayer systems described by the extended
Falicov-Kimball model. Evaluating the anomalous Green's function and momentum
distribution function of the pairs, and thereby analyzing the dependence of the
exciton binding energy, condensation amplitude, and coherence length on the
Coulomb interaction strength, we demonstrate a crossover between a BCS-like
electron-hole pairing transition and a Bose-Einstein condensation of tightly
bound preformed excitons. We furthermore show that a mass imbalance between
electrons and holes tends to suppress the condensation of excitons.
