3-Substituted vinyl cephalosporin derivatives represented by the following formula: ##STR1## wherein R.sup.1 represents a hydroxyl or lower alkoxyl group, X represents a nitrogen atom or a group represented by the formula --CH.dbd., R.sup.2 represents a carboxyl group or a carboxyl group protected with a protecting group, and R.sup.3 is as defined herein, and pharmaceutically acceptable salts thereof are potent antibacterial agents. Processes for their preparation, intermediates in such processes, and antibacterial compositions containing them as active ingredients are also described.