Imino sugars of the piperidine and pyrrolidine types can be specifically obtained when protected 5-amino-5-deoxyfuranopentoses, 5-amino-5-deoxyfuranohexoses, 6-amino-6-deoxyfuranohexoses, and 6-amino-6-deoxypyranohexoses undergo a tandem alkoxy radical beta-fragmentation-intramolecular cyclization reaction. The reaction is promoted by the system: iodosylbenzene-iodine under mild conditions. The tert-butoxycarbonyl, benzyloxycarbonyl, and diphenylphosphinoyl radicals have been studied as amino-protecting groups. Using this methodology, polyhydroxylated pyrrolidines of the D-erythrofuranoses 34 and 35, D-threofuranose 36, L-xylofuranose 42, and D-arabinofuranose 43 series and polyhydroxylated piperidines of the D-arabinopyranose type 37 and 38 were obtained.