Thermoplastic composition comprising at least a mixture of three polymers, in which: - the first polymer, present in the composition at between 10% and 70% by weight, consists of a polyamide-grafted polymer having a polyolefin trunk containing a residue of at least one unsaturated monomer and a plurality of polyamide grafts, in which: - the polyamide grafts are attached to the polyolefin trunk via the unsaturated monomer residue comprising a function that is capable of reacting via a condensation reaction with a polyamide bearing at least one amine end group and/or at least one carboxylic acid end group, - the unsaturated monomer residue is attached to the trunk by grafting or copolymerization, - the polyamide grafts represent from 10% to 60% and preferably from 15% to 55% by weight of said polyamide-grafted polymer, - the second polymer, present in the composition in an amount of at least 10% by weight, consists of a copolymer of ethylene and of an unreactive or non-functionalized comonomer whose flexural elastic modulus is less than 250 MPa at 23°C and which has a crystal melting point of between 60°C and 120°C, - the third polymer, present in the composition at between 3% and 45% by weight of said composition, consisting of a functionalized polyolefin comprising a copolymer of at least one alpha-olefin, such as ethylene or propylene, with at least one comonomer bearing a reactive function, and at least one other comonomer not bearing a reactive function, chosen from an alpha-olefin different from the abovementioned alpha-olefin, a diene, an unsaturated carboxylic acid ester, and a vinyl ester of a carboxylic acid, characterized in that the polyamide grafts of the abovementioned first polymer have a glass transition temperature and a melting point of less than or equal to 160°C, and in that the content of polyamide grafts in said first polymer represents from 3% to 15% and preferably between 5% and 12.5% by weight of the thermoplastic composition. - the first polymer, present in the composition at between 10% and 70% by weight, consists of a polyamide-grafted polymer having a polyolefin trunk containing a residue of at least one unsaturated monomer and a plurality of polyamide grafts, in which: - the polyamide grafts are attached to the polyolefin trunk via the unsaturated monomer residue comprising a function that is capable of reacting via a condensation reaction with a polyamide bearing at least one amine end group and/or at least one carboxylic acid end group, - the unsaturated monomer residue is attached to the trunk by grafting or copolymerization, - the polyamide grafts represent from 10% to 60% and preferably from 15% to 55% by weight of said polyamide-grafted polymer, - the polyamide grafts are attached to the polyolefin trunk via the unsaturated monomer residue comprising a function that is capable of reacting via a condensation reaction with a polyamide bearing at least one amine end group and/or at least one carboxylic acid end group, - the unsaturated monomer residue is attached to the trunk by grafting or copolymerization, - the polyamide grafts represent from 10% to 60% and preferably from 15% to 55% by weight of said polyamide-grafted polymer, - the second polymer, present in the composition in an amount of at least 10% by weight, consists of a copolymer of ethylene and of an unreactive or non-functionalized comonomer whose flexural elastic modulus is less than 250 MPa at 23°C and which has a crystal melting point of between 60°C and 120°C, - the third polymer, present in the composition at between 3% and 45% by weight of said composition, consisting of a functionalized polyolefin comprising a copolymer of at least one alpha-olefin, such as ethylene or propylene, with at least one comonomer bearing a reactive function, and at least one other comonomer not bearing a reactive function, chosen from an alpha-olefin different from the abovementioned alpha-olefin, a diene, an unsaturated carboxylic acid ester, and a vinyl ester of a carboxylic acid, characterized in that the polyamide grafts of the abovementioned first polymer have a glass transition temperature and a melting point of less than or equal to 160°C, and in that the content of polyamide grafts in said first polymer represents from 3% to 15% and preferably between 5% and 12.5% by weight of the thermoplastic composition.