A facile construction of a heteropolycyclic framework is developed by exploiting the dual functionalization of allene. On treatment of phenethyl alcohol or amine bearing, a terminal allene with the Bronsted acid, two consecutive reactions to allene, nucleophilic addition of heteroatom and the Friedel-Crafts reaction, occurred to give 2-oxa- or azabicyclo[2.2.2]octane skeleton.