  We study the bilayer quantum Hall system at total filling factor \nu_T = 1
within a bosonization formalism which allows us to approximately treat the
magnetic exciton as a boson. We show that in the region where the distance
between the two layers is comparable to the magnetic length, the ground state
of the system can be seen as a finite-momentum condensate of magnetic excitons
provided that the excitation spectrum is gapped. We analyze the stability of
such a phase within the Bogoliubov approximation firstly assuming that only one
momentum Q0 is macroscopically occupied and later we consider the same
situation for two modes \pm Q0. We find strong evidences that a first-order
quantum phase transition at small interlayer separation takes place from a
zero-momentum condensate phase, which corresponds to Halperin 111 state, to a
finite-momentum condensate of magnetic excitons.
