Method for a sealed connection of a connector to a heat exchanger of the coaxial tubular type, in particular for a motor vehicle air-conditioning circuit, this exchanger comprising two coaxial tubes, respectively internal and external, the external tube defining around the internal tube, a first annular channel for the circulation of a first fluid, and the internal tube defining a second internal channel for the circulation of a second fluid, the tubes being independent from one another and one of the tubes comprising projections in abutment on the other of the tubes to keep the tubes at a distance from one another, the connector comprising a material block comprising two cavities (36, 38) for the passage of the fluids communicating respectively with the channels (C1, C2) of the exchanger, characterised in that it comprises the following successive steps: a) a free end (14b1) of the external tube is mounted in or on the connector, b) the external tube is directly secured to the connector, c) the internal tube is inserted in the external tube until a free end (14a1) of the internal tube is mounted in a blind manner in the connector, this mounting without welding ensuring a sealing between the internal tube and the connector, and d) the internal and external tubes are directly secured against one another, by plastic deformation of at least one of the tubes (14a, 14b), to avoid relative displacements. this exchanger comprising two coaxial tubes, respectively internal and external, the external tube defining around the internal tube, a first annular channel for the circulation of a first fluid, and the internal tube defining a second internal channel for the circulation of a second fluid, the tubes being independent from one another and one of the tubes comprising projections in abutment on the other of the tubes to keep the tubes at a distance from one another, the connector comprising a material block comprising two cavities (36, 38) for the passage of the fluids communicating respectively with the channels (C1, C2) of the exchanger, characterised in that it comprises the following successive steps: a) a free end (14b1) of the external tube is mounted in or on the connector, b) the external tube is directly secured to the connector, c) the internal tube is inserted in the external tube until a free end (14a1) of the internal tube is mounted in a blind manner in the connector, this mounting without welding ensuring a sealing between the internal tube and the connector, and d) the internal and external tubes are directly secured against one another, by plastic deformation of at least one of the tubes (14a, 14b), to avoid relative displacements. a) a free end (14b1) of the external tube is mounted in or on the connector, b) the external tube is directly secured to the connector, c) the internal tube is inserted in the external tube until a free end (14a1) of the internal tube is mounted in a blind manner in the connector, this mounting without welding ensuring a sealing between the internal tube and the connector, and d) the internal and external tubes are directly secured against one another, by plastic deformation of at least one of the tubes (14a, 14b), to avoid relative displacements.