The invention relates to a process for the preparation of a block copolymer comprising a sequence successively comprising a semicrystalline and/or hydrolysable block, an elastomeric block and an amorphous block, comprising the following stages: a) a stage of 1,2-addition, to a terminal ethylenic group of a semicrystalline and/or hydrolysable polymer, of an alkoxyamine which can correspond to the following formula (II): b) a stage of addition, to the medium resulting from stage a), of one or more monomers which are precursors of the elastomeric block, in return for which a semicrystalline and/or hydrolysable block-b-elastomeric block diblock copolymer is obtained; c) a stage of addition, to the medium resulting from stage b), of one or more monomers which are precursors of the amorphous block, in return for which the semicrystalline and/or hydrolysable block-b-elastomeric block-b-amorphous block triblock copolymer is obtained. Application of the copolymers obtained as impact modifier for amorphous matrices.