Thirty-one melon accessions were screened for resistance to the begomoviruses melon Melon chlorotic mosaic virus (MeCMV) and tomato Tomato leaf curl New Delhi virus (ToLCNDV). Five accessions presented nearly complete resistance to both viruses. Accession IC-274014, showing the highest level of resistance to both viruses, was crossed with the susceptible cultivar ‘Védrantais’. The F1, F2, F3/F4 and both back-cross progenies were mechanically inoculated with MeCMV. Plants without symptoms nor virus detection by ELISA and/or PCR were considered as resistant. The segregations were compatible with two recessive and one dominant independent genes simultaneously required for resistance. Inheritance of resistance to ToLCNDV in the F2 was best explained by one recessive gene and two independent dominant genes simultaneously required. Some F3 and F4 families selected for resistance to MeCMV were also resistant to ToLCNDV, suggesting that common or tightly linked genes were involved in resistance to both viruses. We propose the names begomovirus resistance-1 and Begomovirus resistance-2 for these genes (symbols bgm-1 and Bgm-2). Resistance to MeCMV in IC-274014 was controlled by bgm-1, Bgm-2 and the recessive gene melon chlorotic mosaic virus resistance (mecmv); resistance to ToLCNDV was controlled by bgm-1, Bgm-2 and the dominant gene Tomato leaf curl New Delhi virus resistance (Tolcndv).