By using the multifiber spectrograph FLAMES mounted at the ESO-VLT , we have obtained high-resolution spectra for 18 giant stars , belonging to 3 old globular clusters of the Large Magellanic Cloud ( namely NGC 1786 , 2210 and 2257 ) . While stars in each cluster showed quite homogeneous iron content , within a few cents of dex ( the mean values being Fe/H ] = –1.75 \pm 0.01 dex , –1.65 \pm 0.02 dex and –1.95 \pm 0.02 dex for NGC 1786 , 2210 and 2257 , respectively ) , we have detected significant inhomogeneities for the [ Na/Fe ] , [ Al/Fe ] , [ O/Fe ] and [ Mg/Fe ] abundance ratios , with evidence of [ O/Fe ] vs [ Na/Fe ] and [ Mg/Fe ] vs [ Al/Fe ] anticorrelations . The trends detected nicely agree with those observed in Galactic Globular Clusters , suggesting that such abundance anomalies are ubiquitous features of old stellar systems and they do not depend on the parent galaxy environment . In NGC 1786 we also detected two extreme O-poor , Na-rich stars . This is the first time that a firm signature of extreme chemical abundance anomalies has been found in an extragalactic stellar cluster .