The invention relates to a process for trapping a free monomer which has not reacted by copolymerization or by grafting comprising at least one epoxide functional group in a thermoplastic composition based on ethylene and/or on propylene and based on at least one monomer comprising at least one epoxide functional group, the said process comprising the following stages:preparation of the said thermoplastic composition,addition of a sufficient amount of a solid trapping additive exhibiting, at its surface, sites with a basic nature within the Lewis or Bronsted meaning.The trapping additive is a porous zeolite, the diameter of the pores of which is between 5 and 15 angstroms, preferably between 6 and 13 angstroms. The invention also relates to the composition obtained by such a process and to the blends comprising such a composition.