Novel antibacterially active 1-cyclopropyl-1,4-dihydro-4-oxo-7-[4-(2-oxo-1,3-dioxol-4-yl-methyl)-1-piperazinyl]-3-quinolinecarboxyic acids of the formula in which ##STR1## R is hydrogen or, together with R.sup.1, forms an alkylene radical with 2 or 3 carbon atoms,R.sup.1 is hydrogen, alkyl with 1 to 4 carbon atom or phenyl,R.sup.2 and R.sup.3 each independently is hydrogen, methyl, ethyl, cyclohexyl, methylene-dioxphenyl, furyl, tetrahydrofuryl or thienyl; or phenyl which is optionally mono-, di or tri-substituted by fluorine, chlorine, bromine, methyl, phenyl, cyano, hydroxyl, ethoxy, benzyloxy, amino, methylamino, dimethylamino, piperidino or nitro,X.sup.1 is hydrogen, halogen, or nitro, andX.sup.2 is hydrogen or halogen,or pharmaceutically acceptable hydrates, acid addition salts, alkali metal salts or alkaline earth metal salts thereof.