Abstract: Disclosed is a process for the preparation of a 5-hydroxy-3-ketoester derivative of the formula: ##STR1## in which R.sup.1 represents an alkyl group, an alkenyl group, an alkynyl group, an aryl group or a heterocyclic group, and R.sup.2 represents an alkyl group or an aryl group, which comprises causing the reaction of an aldehyde compound of the formula R.sup.1 CHO in which R.sup.1 has the meanings as defined above and diketene in the presence of a metal compound selected from a titanium or aluminum compound having at least one group of --OR.sup.3 in which R.sup.3 represents an alkyl group or an aryl group. Further, a process for the preparation of an optically active substance of the 5-hydroxy-3-ketoester derivative causing the reaction of the above compounds in the presence of the metal compound and optically active Schiff base or a complex compound obtained by reacting the metal compound with the optically active Schiff base, also is disclosed.