The invention relates to a flexible thermoplastic composition resistant to the ageing effects of oil, said composition comprising a grafted copolymer containing polyamide blocks and consisting of a polyolefin backbone and at least one polyamide graft. According to the invention, the grafts are attached to the core by the residues of an unsaturated monomer (X) having a function that can react with a polyamide comprising an amine end or a carboxylic acid end; the residues of the unsaturated monomer (X) are attached to the backbone by grafting or copolymerization from the double bond thereof; and the composition comprises between 40 to 90 wt % of the polyolefin core comprising the unsaturated monomer (X); between 5 to 40 wt % of polyamide grafts; and between 5 to 40% of at least one polymer selected from a saponified ethylene/vinyl acetate copolymer and a polyamide.