Abstract: Telechelic or semi-telechelic polymers, the average composition of which has the (Y).sub.y formulaV--(X).sub.x --(Y).sub.y --ZwhereinV is a hydrogen atom or Z,X is the radical originating from an ethylenically monomer carrying a polymerizable >C = C< group and at least one other reactant group selected from the group consisting of OH.sub.2 ##EQU1## (R and R' being a hydrogen atom or a lower alkyl radical), COOH or anhydride and ##EQU2## Y is the radical originating from an ethylenically unsaturated monomer carrying only a >C = C< group,Z is a hydrocarbon radical carrying at least one reactive group selected from OH, COOH and NH.sub.2,x is a number between 0 to 10,y is the required number of molecules of Y to ensure that the molecular weight of the polymer chain is between 2000 and 8000,The x radicals X and the y radicals Y being statistically distributed along the --(X).sub.x --(Y).sub.