Methods of producing carboxylic acid ester derivatives of formulae (I) and (II), which are useful, for instance, as intermediates for producing an anti-hypercholesterolemic agent having an inhibitory effect on HMG-CoA Reductase: ##STR1## wherein R.sup.1 and R.sup.2 are independently a protective group for hydroxyl group, or R.sup.1 and R.sup.2 integrally constitute a protective group for hydroxyl groups; R.sup.3 is an alkyl group, or an aryl group; and R.sup.4 is a substituted aryl group, a substituted heterocyclic group, a substituted vinyl group, or a substituted cycloalkenyl group; and ##STR2## wherein R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are respectively the same as defined in the above formula (I), are disclosed. In addition, intermediates for use in these methods of producing the carboxylic acid ester derivatives are disclosed.