Polycyclic phthalazines, in particular 2-substituted maduraphthalazines (10,12,15,16-tetrahydroxy-8-methoxy-11-methyl-1,9,14-trioxo-1,2,6,7,9,14-hexahydronaphthaceno-1,2-g-phthalazines), of formula I and their use against gram-positive bacterial strains, particularly against multi-resistant staphylococci (MRSA) and against glycopeptide-resistant, for example vancomycin-resistant, enterococci. The polycyclic phthalazines are thus suitable for preparing anti-bacterially effective pharmaceutical compositions. In formula I, R.sup.1 is carboxyalkyl or carboxyaryl, and R.sup.2 and R.sup.3 represent H or acyl (for example CO-alkyl or COO-alkyl), with R.sup.1 being different from optionally substituted carboxyphenyl when R.sup.3 represents C.sub.1-8 alkanoyl. The invention also relates to salts, amides and esters of compounds of formula I.