There are only a handful of known star clusters in the LMC that are genuinely old , i.e . of similar age to the globular star clusters in the Milky Way . We report the first results of a color-magnitude diagram survey of 25 candidate old LMC clusters , which were uncovered by means of integrated UBV photometry and CaII triplet spectroscopy during previous investigations . The photometry was carried out with the Washington system C,T _ { 1 } filters on the Cerro Tololo 0.9m telescope . For almost all of the sample , it was possible to reach the turnoff region , and in many clusters we have several magnitudes of the main sequence . The efficiency and efficacy of the technique are demonstrated by our deep CMD for ESO 121-SC03 ( used as a control and calibrator ) , which clearly shows a magnitude of main sequence for this \approx 9 Gyr old object in a total of < 1 hour of integration time . Age estimates based on the magnitude difference \delta T _ { 1 } between the giant branch clump and the turnoff , calibrated using standard clusters , revealed that no new old clusters were found . The candidates turned out to be of intermediate age ( 1-3 Gyr ) ( we can not rule out old ages for NGC 1928 and NGC 1939 since the turnoff was not reached for these compact clusters in crowded bar fields ) . We show that the apparently old ages as inferred from integrated UBV colors can be explained by a combination of stochastic effects produced by bright stars and by photometric errors for faint clusters lying in crowded fields . The relatively metal poor ( [ Fe / H ] \sim - 1.0 ) candidates from the CaII triplet spectroscopy also turned out to be of intermediate age . This , combined with the fact that they lie far out in the disk , yields interesting constraints regarding the formation and evolution of the LMC disk . We also study the age distribution of intermediate age and old clusters considering not only the present \delta T _ { 1 } parameter , but also \delta V and \delta R measured in CMDs from the literature . This homogeneous set of accurate relative ages allows us to make an improved study of the history of cluster formation/destruction for ages > 1 Gyr . We confirm previous indications that there was apparently no cluster formation in the LMC during the period from 3-8 Gyr ago , and that there was a pronounced epoch of cluster formation beginning 3 Gyrs ago that peaked at about 1.5 Gyrs ago . Our results suggest that there are few , if any , genuine old clusters in the LMC left to be found .