  (...) We search for an explanation of the disagreement between the observed
integrated colours of 650 local Galactic clusters and the theoretical colours
of present-day SSP models. We check the hypothesis that the systematic offsets
between observed and theoretical colours, which are $(B$$-$$V)\approx 0.3$ and
$(J$$-$$K_s)\approx 0.8$, are caused by neglecting the discrete nature of the
underlying mass function. Using Monte Carlo simulations, we construct
artificial clusters of coeval stars taken from a mass distribution defined by
an Salpeter initial mass function (IMF) and compare them with corresponding
"continuous-IMF" SSP models. If the discreteness of the IMF is taken into
account, the model fits the observations perfectly and is able to explain
naturally a number of red "outliers" observed in the empirical colour-age
relation. We find that the \textit{systematic} offset between the continuous-
and discrete-IMF colours reaches its maximum of about 0.5 in $(B$$-$$V)$ for a
cluster mass $M_c=10^2 m_\odot$ at ages $\log t\approx 7$, and diminishes
substantially but not completely to about one hundredth of a magnitude at $\log
t >7.9$ at cluster masses $M_c> 10^5 m_\odot$. At younger ages, it is still
present even in massive clusters, and for $M_c \leqslant 10^4 m_\odot$ it is
larger than 0.1 mag in $(B$$-$$V)$. Only for very massive clusters ($M_c>10^6
m_\odot$) with ages $\log t< 7.5$ is the offset small (of the order of 0.04
mag) and smaller than the typical observational error of colours of
extragalactic clusters.
