  In this paper we present a study of an exciton system where electrons and
holes are confined in double quantum well structures. The dominating
interaction between excitons in such systems is a dipole - dipole repulsion. We
show that the tail of this interaction leads to a strong correlation between
excitons and substantially affects the behavior of the system. Making use of
qualitative arguments and estimates we develop a picture of the exciton -
exciton correlations in the whole region of temperature and concentration where
excitons exist. It appears that at low concentration degeneracy of the excitons
is accompanied with strong multi-particle correlation so that the system cannot
be considered as a gas. At high concentration the repulsion suppresses the
quantum degeneracy down to temperatures that could be much lower than in a Bose
gas with contact interaction. We calculate the blue shift of the exciton
luminescence line which is a sensitive tool to observe the exciton - exciton
correlations.
