A process for the sequential and convergent preparation of ordered block copolymers comprising at least one non-polar and one polar polymer block, characterized in that the non-polar block is built up via a living sequential anionic polymerization by means of a Li-organyl initiator having a pKa greater than or equal to 45 from monomers selected from the group consisting of conjugated dienes, styrene, vinylsilane, vinylnaphthalene, vinylmetallocene, their derivatives or mixtures thereof and the polar block is a polymer block having a molecular weight greater than or equal to 350 g/mol and less than or equal to 5000 g/mol and being composed of monomers selected from the group consisting of C2-C10 oxacyclo compounds, their derivatives or mixtures of at least two different monomers thereof, the polar polymer block being covalently linked in a convergent manner to the non-polar block anion via an epoxy functionalization of one of the monomers of the polar block, obtained via a reaction of this monomer with epichlorohydrin, in a non-polar solvent in the presence of free Li ions.