  We investigate the influence of Asymptotic Giant Branch stars on integrated
colours of star clusters of ages between ~100 Myr and a few gigayears, and
composition typical for the Magellanic Clouds. We use state-of-the-art stellar
evolution models that cover the full thermal pulse phase, and take into account
the influence of dusty envelopes on the emerging spectra. We present an
alternative approach to the usual isochrone method, and compute integrated
fluxes and colours using a Monte Carlo technique that enables us to take into
account statistical fluctuations due to the typical small number of cluster
stars. We demonstrate how the statistical variations in the number of
Asymptotic Giant Branch stars and the temperature and luminosity variations
during thermal pulses fundamentally limit the accuracy of the comparison (and
calibration, for population synthesis models that require a calibration of the
Asymptotic Giant Branch contribution to the total luminosity) with star cluster
integrated photometries. When compared to observed integrated colours of
individual and stacked clusters in the Magellanic Clouds, our predictions match
well most of the observations, when statistical fluctuations are taken into
account, although there are discrepancies in narrow age ranges with some (but
not all) set of observations.
