A reaction of cycloalkanone, alkanone and alkyl aryl ketone ketals with H2O2 catalyzed by boron trifluoride etherate and boron trifluoride–methanol complexes was studied. A new versatile method for the synthesis of bishydroperoxides and their derivatives, viz. 1, 1′- dihydroperoxyperoxides and 1, 2, 4, 5-tetraoxacyclohexanes, was developed based on this reaction.