The present invention is a composition comprising by weight: 70 to 96% of at least one polyamide chosen from PA-11, PA-12, aliphatic polyamides resulting from the condensation of an aliphatic diamine having from 6 to 12 carbon atoms and an aliphatic diacid having from 9 to 12 carbon atoms, and 11/12 copolyamides having either more than 90% of nylon-11 units or more than 90% of nylon-12 units; 4 to 10% of a plasticizer; 0 to 25% of an NBR or HnullNBR elastomer; and the sum of the amount of plasticizer and the amount of elastomer is between 4 and 30%. These compositions can be manufactured by melt-blending the various constituents using standard techniques for thermoplastics. They are particularly useful for pipes used in the operation of offshore oil and gas fields. They exhibit very good ageing resistance. They are also useful for simpler pipes in motor vehicles, these compositions withstanding the ageing caused by the temperature under the bonnet of motor vehicles and the nature of the fluids transported. The invention also relates to pipes comprising at least one layer of this composition. These are either pipes used offshore or simpler pipes for motor vehicles.