System for cooling air, referred to as bleed air, drawn from an engine (6, 7) of an aircraft during use of the system and intended to supply air at a controlled temperature to at least one item of equipment, characterised in that said system comprises: - an air circuit adapted to provide fluid communication between means for drawing bleed air from said engine (6, 7) and said item of equipment, said air circuit comprising at least one cylindrical conduit for the flow of bleed air, adapted to be arranged in a first zone of the aircraft, - a first cylindrical heat exchanger for air/air cooling fitted into said cylindrical conduit for the flow of bleed air, said first exchanger comprising a primary circuit adapted to be supplied by said bleed air, and a secondary circuit, extending generally parallel to the primary circuit, adapted to be supplied by a source of cold air, said primary circuit and secondary circuit being configured to be able to ensure heat exchanges between the air flow of the primary circuit and the air flow of the secondary circuit, so as to form a first cooling stage for the bleed air drawn from the engine, - a second heat exchanger for air cooling, adapted to be arranged in a second zone of the aircraft, said second heat exchanger comprising a primary circuit adapted to be supplied by the air from the primary circuit of said first cooling stage, and a secondary circuit, adapted to be supplied by a source of cold fluid, said circuits being configured to be able to ensure heat exchanges between the air flow of the primary circuit and the fluid flow of the secondary circuit, so as to form a second cooling stage for the bleed air drawn from the engine, said air flow exiting this second cooling stage being adapted to supply said item of equipment. - an air circuit adapted to provide fluid communication between means for drawing bleed air from said engine (6, 7) and said item of equipment, said air circuit comprising at least one cylindrical conduit for the flow of bleed air, adapted to be arranged in a first zone of the aircraft, - a first cylindrical heat exchanger for air/air cooling fitted into said cylindrical conduit for the flow of bleed air, said first exchanger comprising a primary circuit adapted to be supplied by said bleed air, and a secondary circuit, extending generally parallel to the primary circuit, adapted to be supplied by a source of cold air, said primary circuit and secondary circuit being configured to be able to ensure heat exchanges between the air flow of the primary circuit and the air flow of the secondary circuit, so as to form a first cooling stage for the bleed air drawn from the engine, - a second heat exchanger for air cooling, adapted to be arranged in a second zone of the aircraft, said second heat exchanger comprising a primary circuit adapted to be supplied by the air from the primary circuit of said first cooling stage, and a secondary circuit, adapted to be supplied by a source of cold fluid, said circuits being configured to be able to ensure heat exchanges between the air flow of the primary circuit and the fluid flow of the secondary circuit, so as to form a second cooling stage for the bleed air drawn from the engine, said air flow exiting this second cooling stage being adapted to supply said item of equipment.