Abstract: A process for the preparation of a 7-acylamino-3-hydroxy-2-cephem-4-carboxylic acid, 7-acylamino-3-hydroxy-1-dethia-1-oxa-3-cephem-4-carboxylic acid or derivative thereof of the general formula ##STR1## in which R.sup.1 is hydrogen or optionally substituted alkyl, alkenyl, alkinyl, aralkyl, aryl, heteroaryl, heteroaralkyl, aryloxyalkyl, heteroaryloxyalkyl, alkoxyalkyl, arylthioalkyl, heteroarylthioalkyl, alkylthioalkyl, alkoxy, aryloxy, alkylthio or arylthio,R.sup.2 is hydrogen, a carboxy-protective group or a pharmaceutically useful ester radical, andX is sulphur or oxygen,which comprises:(a) reacting a compound of the formula ##STR2## with (i) a compound of the formula ##STR3## in which R.sup.2 and X have the abovementioned meaning and Y represents diazo (N.sub.2) or hydrogen (H.sub.2) in an inert solvent in the presence of a Lewis acid or proton acid catalyst, or(ii) a compound of the formulaHX--CH.sub.2 --C.tbd.C--COOR.sup.