We describe here the synthesis and biological evaluation of a series of benzo[b]naphthyridones, a new family of tricyclic antibacterial compounds that have a gram-positive spectrum of activity. RP60556A, one of the most potent of these compounds, is bactericidal against multiresistant cocci, especially multiresistant Staphylococcus aureus strains. Its physico-chemical and biological properties make it particularly suitable for topical antibacterial use.