Drainage device intended to be installed on a construction having an external surface and provided with a discharge channel, in particular on a roof of a building or a terrace, in order to discharge in particular the rainwater, comprising: - a drainage head (11; 109) comprising an external wall (12; 110) delimiting a recovery space (13; 111) and having a discharge passage (14; 112) around which the external wall has a support shoulder (15; 115) able to bear on the external surface of the construction, around the discharge channel, and at least one recovery passage (17; 119); and - a mounting element comprising a support or attachment element (23; 121) capable of being engaged inside the discharge channel and of abutting against the peripheral wall of the discharge channel, and a biasing element (24; 124) connecting the drainage head and the support or attachment element, the support or attachment element (23; 121) comprising a plurality of elastically deformable arms (25; 122) capable of deforming non-permanently under the action of an external force and of tending to resume its shape before deformation after the external force is stopped, and having ends able to bear against the peripheral wall of the discharge channel, at points spaced apart in the circumferential direction, in a position deformed counter to their elasticity, - the biasing element (24; 124) being able to act on the support or attachment element, so that the ends of the arms (25; 122) of the support or attachment element, abutting against the peripheral wall of the discharge channel, under the effect of the biasing element, are able to hold said support shoulder of the drainage head in abutment on the external surface of the construction, - the support or attachment element comprise a central portion provided with said arms at the periphery thereof, - in the engaged position of the support or attachment element (23; 121) inside the discharge channel, the arms (25; 122) of said element being curved and the ends abutting against the peripheral wall of the discharge channel and being offset axially with respect to the central portion of the support or attachment element on the same side as the drainage head (11; 109), - the biasing element (24; 124) cooperating with the central portion of the support or attachment element by screwing so as to increase the curvature of said arms during screwing. - a drainage head (11; 109) comprising an external wall (12; 110) delimiting a recovery space (13; 111) and having a discharge passage (14; 112) around which the external wall has a support shoulder (15; 115) able to bear on the external surface of the construction, around the discharge channel, and at least one recovery passage (17; 119); and - a mounting element comprising a support or attachment element (23; 121) capable of being engaged inside the discharge channel and of abutting against the peripheral wall of the discharge channel, and a biasing element (24; 124) connecting the drainage head and the support or attachment element, the support or attachment element (23; 121) comprising a plurality of elastically deformable arms (25; 122) capable of deforming non-permanently under the action of an external force and of tending to resume its shape before deformation after the external force is stopped, and having ends able to bear against the peripheral wall of the discharge channel, at points spaced apart in the circumferential direction, in a position deformed counter to their elasticity, - the biasing element (24; 124) being able to act on the support or attachment element, so that the ends of the arms (25; 122) of the support or attachment element, abutting against the peripheral wall of the discharge channel, under the effect of the biasing element, are able to hold said support shoulder of the drainage head in abutment on the external surface of the construction, - the support or attachment element comprise a central portion provided with said arms at the periphery thereof, - in the engaged position of the support or attachment element (23; 121) inside the discharge channel, the arms (25; 122) of said element being curved and the ends abutting against the peripheral wall of the discharge channel and being offset axially with respect to the central portion of the support or attachment element on the same side as the drainage head (11; 109), - the biasing element (24; 124) cooperating with the central portion of the support or attachment element by screwing so as to increase the curvature of said arms during screwing.