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.
