  The discovery of multiple MSs in NGC2808 and Omega Centauri, and multiple
SGBs in NGC1851 and NGC6388 has challenged the long-held paradigm that GCs
consist of simple stellar populations. This picture has been further
complicated by recent studies of the LMC intermediate-age clusters, where the
MSTO was found to be bimodal or broadened. We have undertaken a study of
archival HST images of LMC and SMC clusters with the aim of measuring the
frequency of clusters with evidence of multiple or prolonged star formation
events and determining their main properties. In this paper, we analyse the CMD
of 16 intermediate-age LMC clusters. We find that 11 clusters show an anomalous
spread (or split) in color and magnitude around the MSTO. We demonstrate that
the observed feature is unequivocally associated to the clusters and that it is
not an artifact due to photometric errors, differential reddening or binaries.
We confirm that NGC 1806 and NGC 1846 clearly exhibit two distinct MSTOs and
observe, for the first time, a double MSTO in NGC 1751. In these three clusters
the population corresponding to the brighter MSTO includes more than two-thirds
of cluster stellar population. We confirm the presence of multiple stellar
populations in NGC 1783 and suggest that the MSTO of this cluster is formed by
two distinct branches. In 7 clusters (ESO057-SC075, HODGE7, NGC1852, NGC1917,
NGC1987, NGC2108, and NGC2154) we observed an intrinsic broadening of the MSTO
that may suggest that these clusters have experienced a prolonged period of
star formation (150-250 Myr). The CMDs of IC2146, NGC1644, NGC1652, NGC1795 and
NGC1978 show no evidence of spread or bimodality. In summary 70$\pm$25% of our
sample are not consistent with the simple, single stellar population hypotesis.
