A cephalosporin derivative of the formula: ##STR1## in which R.sup.0 is a hydrogen atom or a methyl radical, R.sup.1 is any one of the C-3 substituents from antibacterially-active cephalosporins known in the art; R.sup.2 is any one of the C-4 substituents from antibacterially-active cephalosporins known in the art; R.sup.3 is a hydrogen atom or a 1-6C alkoxy or 1-6C alkylthio radical; X.sup.1 is a sulphur or oxygen atom, a CH.sub.2 radical or a radical of the formula NR.sup.7 in which R.sup.7 is a hydrogen atom, a 1-6C alkyl, formyl or benzyl radical; X.sup.2 is a nitrogen atom or a radical of the formula N.sup..sym. -R.sup.7 ; R.sup.4 and R.sup.7, and R.sup.5 and R.sup.6 are a variety of substituents which are described in the specification; and the pharmaceutically-acceptable acid- or base-addition salts thereof. Pharmaceutical compositions, manufacturing processes and intermediates are also described.