In the free-radical addition of a number of organohalogen reagents to cyclic alkenes and dienes in the presence of copper(I) halides the composition of the reaction products is governed by the stage of a fast halogen transfer from the copper derivative to the alkyl radical. Under these conditions in contrast to the free-radical addition reactions initiated by UV light or peroxide initiators the intramolecular rearrangements are suppressed, the stereoselectivity of the reaction changes, and also some adducts contain halogen atoms different from those present in the organohalogen reagent employed.