Integrated (B-V)_0_ and (U-B)_0_ colours and synthetic HR diagrams of stellar clusters as a function of the age are obtained with the aid of stellar models that incorporate the effects of convective overshoot all over their major evolutionary phases. Effects of stochastic nature in the initial mass function caused by the finite number of stars per cluster, and effects of dispersion in the stellar ages are also taken into account. The resulting theoretical calibrating relationships are presented and some implications for real clusters of different age are outlined. In particular, we derive the age and colour distribution functions (number of clusters per age and colour range) for clusters of the LMC, and discuss the causes of the "gap" in the relation between (B-V) and cluster type by Searle et al. (1980) and/or in the V versus (B-V) diagram, or equivalently the bimodality of the colour distribution function. Over the past few years many suggestions have been advanced to explain the physical causes of the gap: an age gap and/or effects of cluster disruption, sudden reddening of the (B-V) color caused by the appearance for the first time in a cluster of stars in particular evolutionary phases (red and asymptotic giant branches, collapse of loops to a clump). None of these has been however tested on the basis of complete models of photometric synthesis. We find that no unique cause can be singled out, rather the observed colour distribution is the result of several concurrent factors. In brief, the colour distribution can be derived from models of photometric synthesis of star clusters provided the age distribution function and the colour speed are known. The age distribution is obtained from cluster counts per age range as originally proposed by Elson and Fall (1985). This is however modified to incorporate the novel ages derived from stellar models with convective overshoot. The observational age distribution obtained from this procedure is the end product of the history of cluster formation and disruption (by various dynamical effects). Finally, the colour speed is simply given by calculating from photometric models a colour age relation. We find that the colour distribution is primarily reflective of the age distribution function, which determines the ratio of the blue to red clusters, whereas the colour speed fixes the location and width of the gap.
