  We present a study of the evolved stellar populations in the dwarf spheroidal
galaxy LeoII, based on JHKs observations obtained with the near-infrared array
WFCAM at the UKIRT telescope. Combining the new data with optical data, we
derived photometric estimates of the distribution of global metallicity [M/H]
of individual red giant stars from their V-Ks colours. We used the new data to
derive the properties of a nearly complete sample of asymptotic giant branch
(AGB) stars in LeoII. Using a near-infrared two-colour diagram, we were able to
obtain a clean separation from Milky Way foreground stars and discriminate
between carbon- and oxygen-rich AGB stars. We simulate the JHKs data with the
TRILEGAL population synthesis code together with the most updated thermally
pulsing AGB models, and using the star formation histories derived from
independent work based on deep HST photometry. After scaling the mass of LeoII
models to the observed number of upper RGB stars, we find that present models
predict too many O-rich TP-AGB stars of higher luminosity due to a likely
under-estimation of either their mass-loss rates at low metallicity, and/or
their degree of obscuration by circumstellar dust. On the other hand, the
TP-AGB models are able to reproduce the observed number and luminosities of
carbon stars satisfactorily well, indicating that in this galaxy the least
massive stars that became carbon stars should have masses as low as ~1 M_sun.
