A compound of the formula: ##STR1## wherein R.sup.1 is an amino group which may be protected, R.sup.3 is a hydrogen atom or an optionally substituted hydrocarbon residue; Z is S, S.fwdarw.O, O or CH.sub.2, R.sup.4 is a hydrogen atom, methoxy group or formamido group, R.sup.13 is a hydrogen atom, methyl group, hydroxyl group or halogen atom and A.sup..sym. is an optionally substituted imidazolium-1-yl group forming a condensed ring at the 2,3- or 3,4-position or a pharmaceutically acceptable salt or ester thereof is novel and has excellent antibacterial activity.