Methods are described herein for converting carbocationically terminated polymers to anionically terminated polymers. These methods comprise: (a) providing a carbocationically terminated polymeric moiety; (b) reacting the carbocationically terminated polymeric moiety with a heterocyclic compound of the formula ##STR00001## where --X-- is selected from --S--, --O--, --NH-- and --NR--, and where R is an alkyl group or an aryl group, thereby providing an end-capped polymeric moiety; and (c) reacting the end-capped polymeric moiety with an organolithium compound to yield an anionically terminated polymeric moiety. Also described are block copolymers in which a first polymer block comprising cationically polymerized monomers is linked to a second polymer block comprising anionically polymerized monomers by a ##STR00002## group, as well as a polymer in which a polymer block comprising cationically polymerized monomers is linked to a halogenated silane residue or a carbosilane residue by a ##STR00003## group.