  We calculate self-consistent models of X-ray irradiated accretion discs in
close binary systems. We show that a point X-ray source powered by accretion
and located in the disc plane cannot modify the disc structure, mainly because
of the self-screening by the disc of its outer regions. Since observations show
that the emission of the outer disc regions in low mass X-ray binaries is
dominated by the reprocessed X-ray flux, accretion discs in these systems must
be either warped or irradiated by a source above the disc plane, or both. We
analyse the thermal-viscous stability of irradiated accretion discs and derive
the stability criteria of such systems. We find that, contrary to the usual
assumptions, the critical accretion rate below which a disc is unstable is
rather uncertain since the correct formula describing irradiation is not well
known.
