A two-step free radical method of synthesis of block copolymers, called TIT-Inifer Method is proposed. In the method, specially designed initiators/transfer agents of the general formula TIT (called herein : TIT-Inifers) are used, [GTAPHICS] where : T represents transfer groups, I is an initiator fragment, and SPACER is any skeleton, that separates the radical center formed at T during transfer reaction from interaction with the initiator fragment. In the first step of the method, a monomer A is polymerized in the presence of a TIT-Inifer at some temperature T-1, at which the initiator fragment of the inifer is stable. In that step the TIT-Inifer acts as a transfer agent, so that the initiator fragment gets incorporated into polymer chain to yield a macroinitiator. In the second step of the method, the macroinitiator is used to initiate polymerization of a monomer B at a temperature T-2, at which the initiator groups of the macroinitiator cleave. Depending of the mode of termination of growing polymer chains, AB-type or ABA-type block copolymers are obtained as the major product, altogether with some amount of homopolymers resulting from side reactions of macroradicals. Two example TIT-Inifers were designed and their application for synthesis of block copolymers was studied. It was found that the TIT-Inifer Method was effective for preparation of block copolymers. Aspects of the mechanism by which the TIT-Inifers attach initiator groups to polymer chains and applicability of the TIT-Inifer Method for large-scale production of block copolymers are discussed.