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(...) We search for an explanation of the disagreement between the observedintegrated colours of 650 local Galactic clusters and the theoretical coloursof present-day SSP models. We check the hypothesis that the systematic offsetsbetween 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 theunderlying mass function. Using Monte Carlo simulations, we constructartificial clusters of coeval stars taken from a mass distribution defined byan Salpeter initial mass function (IMF) and compare them with corresponding"continuous-IMF" SSP models. If the discreteness of the IMF is taken intoaccount, the model fits the observations perfectly and is able to explainnaturally a number of red "outliers" observed in the empirical colour-agerelation. 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 acluster mass $M_c=10^2 m_\odot$ at ages $\log t\approx 7$, and diminishessubstantially but not completely to about one hundredth of a magnitude at $\logt >7.9$ at cluster masses $M_c> 10^5 m_\odot$. At younger ages, it is stillpresent even in massive clusters, and for $M_c \leqslant 10^4 m_\odot$ it islarger than 0.1 mag in $(B$$-$$V)$. Only for very massive clusters ($M_c>10^6m_\odot$) with ages $\log t< 7.5$ is the offset small (of the order of 0.04mag) and smaller than the typical observational error of colours ofextragalactic clusters.

Why Simple Stellar Population models do not reproduce the colours of Galactic open clusters