Cyclic 6-membered to 8-membered 1,2-vinylenedioxy compounds of the general formula I ##STR1## where A is ##STR2## R.sup.1 to R.sup.7 independently of one another are each hydrogen, C.sub.1 -C.sub.8 -alkyl, C.sub.2 -C.sub.16 -alkoxyalkyl, C.sub.2 -C.sub.8 -alkenyl, C.sub.2 -C.sub.8 -alkynyl, C.sub.5 -C.sub.8 -cycloalkyl, aryl, C.sub.7 -C.sub.10 -alkylphenyl, C.sub.7 -C.sub.10 -phenalkyl, C.sub.8 -C.sub.10 -phenalkenyl or a heterocyclic structure, or R.sup.2 and R.sup.3, R.sup.2 and R.sup.4, R.sup.3 and R.sup.4, R.sup.2 and R.sup.6, R.sup.3 and R.sup.6, R.sup.4 and R.sup.5 or R.sup.6 and R.sup.7 together form a cycloaliphatic or heterocyclic ring, and R.sup.1 to R.sup.7 may furthermore carry substituents which are inert under the reaction conditions, and n is 0 or 1, are prepared by a process in which a cyclic 2-oxymethyl-1,3-dioxa compound or one of its derivatives of the general formula II ##STR3## where R.sup.1 to R.sup.7, A and n have the abovementioned meanings, and R.sup.8 is hydrogen or C.sub.1 -C.sub.12 -alkyl, is converted in the presence of an acidic catalyst at from 150.degree. to 450.degree. C. and under from 0.001 to 50 bar, some of the compounds obtained being novel.