The cycloisomerization reactions of allenes bearing cyclic acetal, thioacetal and dithioacetal subunits, when triggered either by the catalytic action of AgSbF₆ or by one equiv. of CF₃COOH, gave rise to four different classes of indeno-fused 1,4-dioxa, oxathia and dithia heterocycles, in most cases as a single diastereomer. Acyclic acetals and dithioacetals are also suitable starting materials in similar transformations yielding 1,2-disubstituted indenes and 1,3-disubstituted 2-alkylideneindanes.