A new method for the synthesis of n-(3-acyloxypropyl)-substituted six- to thirteen-membered alkan-n-olides was developed. The method is based on the H2SO4-catalyzed reactions of oxabicycloalkenes, obtained from 2-(3-acetoxypropyl)cycloalkanes, with H2O2 and formic or acetic acid. The method includes the subsequent transformations of oxabicycloalkenes; into bicyclic hydroperoxides, peroxy ethers, and, at the final stage, into target lactones formed in 56-71% yields. These transformations are carried as a one-pot reaction.