3,7-disubstituted-3-cephem-4-carboxylic acid compounds having bacteriostatic properties and the following formula: ##STR1## in which R.sup.1 is thiadiazolyl or isothiazolyl, each of which may have suitable substituent(s), or thiazolyl; R.sup.2 is hydrogen or lower alkyl; R.sup.3 is carboxy or protected carboxy; R.sup.4 is hydrogen, acyloxy or a heterocyclicthio group which may have suitable substituent(s); and R.sup.5 is hydrogen or lower alkoxy, process for making same and treating infectious diseases therewith.