  We estimate the incidence of multiply-imaged AGNs among the optical
counterparts of X-ray selected point-like sources in the XXL field. We also
derive the expected statistical properties of this sample, such as the redshift
distribution of the lensed sources and of the deflectors that lead to the
formation of multiple images, modelling the deflectors using both spherical
(SIS) and ellipsoidal (SIE) singular isothermal mass distributions. We further
assume that the XXL survey sample has the same overall properties as the
smaller XMM-COSMOS sample restricted to the same flux limits and taking into
account the detection probability of the XXL survey. Among the X-ray sources
with a flux in the [0.5-2] keV band larger than 3.0x10$^{-15}$ erg cm$^{-2}$
s$^{-1}$ and with optical counterparts brighter than an r-band magnitude of 25,
we expect ~20 multiply-imaged sources. Out of these, ~16 should be detected if
the search is made among the seeing-limited images of the X-ray AGN optical
counterparts and only one of them should be composed of more than two lensed
images. Finally, we study the impact of the cosmological model on the expected
fraction of lensed sources.
