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 accretio
n and located in the disc plane cannot modify the disc structure, mainly be
cause of the self-screening by the disc of its outer regions, As observatio
ns show that the emission of the outer disc regions in low-mass X-ray binar
ies is dominated by the reprocessed X-ray flux, accretion discs in these sy
stems 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, cont
rary to the usual assumptions, the critical accretion rate below which a di
sc is unstable is rather uncertain because the correct formula describing i
rradiation is not well known.