The invention relates to thermoplastic polymer compositions in the form of masterbatches, comprising a matrix of an olefinic copolymer obtained from olefinic monomers and at least one alkyl(meth)acrylate monomer, in which exfoliable organophilefilelrs of the lamellar type are dispersed, such as silicates, characterized in that after complete dispersion, the fillers are of nanometer scale with a content of at least 20% by weight with relation to the composition. The invention is further of application for the production of polymeric materials particularly of the polyethylene type, with fillers, the thermomechanical and barrier properties of which are improved.