1,4‐Diphenyl‐2,3‐dioxabicyclo[2.2.1]hept‐5‐ene (2), on treatment with a catalytic amount of trimethylsilyl trifluoromethanesulfonate (Me₃SiOTf) in CH₂Cl₂ at −78°, reacts with excess (−)‐menthone (10) to give (1S,2S,4′aS,5R,7′aS)‐4′a,7′a‐dihydro‐2‐isopropyl‐5‐methyl‐6′,7′‐diphenylspiro[cyclohexane‐1,3′‐[7′H]cyclopenta‐[1,2,4]trioxine] (11) and its (1R,2S,4′aR,5R,7′aR)‐diastereoisomer 12 in a 1:1 ratio and in 21% yield. Repeating the reaction with 1.1 equiv. of Me₃SiOTf with respect to 2 affords 11, 12, and (1S,2S,3′a.R,5R,6′aS)‐3′a,6′a‐dihydro‐2‐isopropyl‐5‐methyl‐3′a‐phenoxy‐5′‐phenylspiro[cyclohexane‐l,2′‐[4′H]cyclopenta[1,3]dioxole] (13) together with its(1R,2S,3′aS,5R,6′aR)‐diastereoisomer 14 in a ratio of 3:3:3:1 and in 56% yield. (+)‐Nopinone(15) in excess reacts with 2 in the presence of 1.1 equiv. of Me₃SiOTf to give a pair of 1,2,4‐trioxanes (16 and 17) analogous to 11 and 12, and a pair of 1,3‐dioxolanes (18 and 19) analogous to 13 and 14, in a ratio of 8:2:3:3 and in 85% yield. (−)‐Carvone and racemic 2‐(tert‐butyl)cyclohexanone under the same conditions behave like 15 and deliver pairs of diastereoisomeric trioxanes and dioxolanes. In general, catalytic amounts of Me₃SiOTf give rise to trioxanes, whereas 1.5 equiv. overwhelmingly engender dioxolanes. Adamantan‐2‐one combines with 2 giving only (4′aRS,7′aRS)‐4′a,7′a‐dihydro‐6′.7′a‐diphenylspiro[adamantane‐2,3′‐[7′H]cyclopenta[1,2,4]trioxine] in 98% yield regardless of the amount of Me₃SiOTf used. The reaction of 1,4‐dipheny 1‐2,3‐dioxabicyclo[2.2.2]oct‐5‐ene (32) with 10 and 1.1 equiv. of Me₃SiOTf produces only the pair of trioxanes 33 and 34 homologous to 11 and 12. Treatment of the (S,S)‐diastereoisomer 33 with Zn and AcOH furnishes (1S,2S)‐1,4‐diphenylcyclohex‐3‐ene‐1,2‐diol. The crystal structures of 11–13 and 16 are obtained by X‐ray analysis. The reaction courses of 10 and the other chiral cyclohexanones with prochiral endoperoxides 2 and 32 to give trioxanes are rationalized in terms of the respective enantiomeric silylperoxy cations which are completely differentiated by the si and re faces of the ketone function. The origin of the 1,3‐dioxolanes is ascribed to 1,2 rearrangement of the corresponding trioxanes, which occurs with retention of configuration of the angular substituent.