A composition is obtained by mixing at least one oligomer A1, which is obtained by copolymerizing at least two monomers functionalized by diol functions with at least one second monomer, with at least one compound A2 having at least two boron ester functions. The compositions exhibit very varied rheological properties depending on the proportion of the compounds A1 and A2 used. A composition is also obtained by mixing at least one lubricating oil with such a composition of associative and exchangeable polymers, and the use of this composition to lubricate a mechanical part.