A cephalosporin derivative having the formula: ##STR1## wherein R.sup.1 is a substituted amino group, X is an alkylene group, R.sup.2 is an aryl or heterocyclic group which may be substituted and R.sup.3 is a hydrogen atom, a negative charge or a residue of an ester which can form a pharmaceutically acceptable ester hydrolyzable in a living body; or a pharmaceutically acceptable salt thereof.