A process for preparing 5-membered ring heterocycles of the general formula I ##STR1## where R.sup.1 is methyl or hydroxyethyl,R.sup.2,R.sup.3,R.sup.4,R.sup.5 and R.sup.6 are hydrogen, C.sub.1 - to C.sub.12 -alkyl, C.sub.2 - to C.sub.12 -alkenyl, aryl, C.sub.3 - to C.sub.8 -cycloalkyl, C.sub.1 - to C.sub.12 -alkoxy, halogen, C.sub.2 - to C.sub.20 -alkoxycarbonylalkyl, C.sub.2 - to C.sub.20 -alkylcarbonyloxy, formyl, C.sub.2 - to C.sub.20 -formylalkyl, benzoyl or --CH(OR.sup.3)(OR.sup.5), or R.sup.3 and R.sup.5 together are a C.sub.2 - to C.sub.7 -alkylene chain which is unsubstituted or monosubstituted to pentasubstituted by R.sup.4 or a .dbd.CH--CH.dbd.CH--CH.dbd. unit which is unsubstituted or monosubstituted to tetrasubstituted by R.sup.4,X is oxygen or N--R.sup.4by reacting 5-membered ring heterocycles of the general formula II ##STR2## where R.sup.2, R.sup.3, R.sup.4, R.sup.5, R.sup.6 and X have the abovementioned meanings and Y is hydrogen, acetyl or C.sub.2 - to C.sub.20 -alkoxycarbonyl, with dimethyl or ethylene carbonate in the presence of a nitrogen-containing base at from 50.degree. to 300.degree. C. and from 0.01 to 50 bar is described.