Processes for preparing block copolymers and the block copolymers prepared therefrom comprising at least two types of homoblock, all belonging to the polysulfone family, wherein each of the said homoblocks has an identical or different molecular weight of at least 1000 and comprises at least 5% of the overall weight of the block copolymer, and wherein the block copolymer has a molecular weight of at least 2000, the process steps comprising preparing each of the aforesaid homoblocks by reacting at least one aromatic diol with at least one aromatic dihalo compound, one of which contains at least one sulfone group, in at least one aprotic solvent in the presence of at least one alkali, optionally in the presence of an azeotropic agent and then reacting the aforesaid homoblocks together in at least an aprotic solvent, optionally followed by end-capping said block copolymer. The invention also relates to the block copolymers themselves, which are useful for molding, extrusion and can also be used as compatibilizers for their high molecular weight homologues.