A method for fixing a flexible hose in a sealed manner to a connector using a crimping collar, wherein: - the following is provided: a. a flexible hose with an open front end, b. a connector including i. a connector body, ii. a tubular nozzle able to receive the front end of the hose, the tubular nozzle including retaining radial projections of the hose as well as a clamping area of the hose, and iii. a temporary accommodation space axially interposed between the tubular nozzle and the connector body and having a maximum radial size of diameter D3, the temporary accommodation space and the clamping are being separated from each other on the connector, and c. a crimping collar for fixing the front end of the flexible hose to the connector, the collar at rest prior to crimping having an inner diameter D0, - the collar is engaged around the connector by the tubular nozzle until the collar circumferentially surrounds at least partially the temporary accommodation space, - the front end of the hose is engaged around the tubular nozzle of the connector until said front end circumferentially surrounds the retaining radial projections and at least part of the clamping area, so that with the crimping collar circumferentially surrounding the temporary accommodation space, the front end of the hose has a first outer diameter D1 at the location of the clamping area and a second outer diameter D2 at the location of the retaining radial projections, the first outer diameter D1 being smaller than the second outer diameter D2, the first outer diameter D1 and the diameter D3 of the maximum radial size being smaller than or equal to the inner diameter D0, and the second outer diameter D2 being larger than or equal to the inner diameter D0, - the collar or the connector is moved in order to leave the temporary accommodation space with regard to the collar and position the crimping collar around at least part of the front end of the hose and substantially opposite the clamping area of the connector, and - the collar is crimped for fixing the open front end of the flexible hose to the connector, knowing that the temporary accommodation space and the clamping area are separated by a separating means chosen among an abutting axial shoulder of the hose or a collar. - the following is provided: a. a flexible hose with an open front end, b. a connector including i. a connector body, ii. a tubular nozzle able to receive the front end of the hose, the tubular nozzle including retaining radial projections of the hose as well as a clamping area of the hose, and iii. a temporary accommodation space axially interposed between the tubular nozzle and the connector body and having a maximum radial size of diameter D3, the temporary accommodation space and the clamping are being separated from each other on the connector, and c. a crimping collar for fixing the front end of the flexible hose to the connector, the collar at rest prior to crimping having an inner diameter D0, a. a flexible hose with an open front end, b. a connector including i. a connector body, ii. a tubular nozzle able to receive the front end of the hose, the tubular nozzle including retaining radial projections of the hose as well as a clamping area of the hose, and iii. a temporary accommodation space axially interposed between the tubular nozzle and the connector body and having a maximum radial size of diameter D3, the temporary accommodation space and the clamping are being separated from each other on the connector, and i. a connector body, ii. a tubular nozzle able to receive the front end of the hose, the tubular nozzle including retaining radial projections of the hose as well as a clamping area of the hose, and iii. a temporary accommodation space axially interposed between the tubular nozzle and the connector body and having a maximum radial size of diameter D3, the temporary accommodation space and the clamping are being separated from each other on the connector, and c. a crimping collar for fixing the front end of the flexible hose to the connector, the collar at rest prior to crimping having an inner diameter D0, - the collar is engaged around the connector by the tubular nozzle until the collar circumferentially surrounds at least partially the temporary accommodation space, - the front end of the hose is engaged around the tubular nozzle of the connector until said front end circumferentially surrounds the retaining radial projections and at least part of the clamping area, so that with the crimping collar circumferentially surrounding the temporary accommodation space, the front end of the hose has a first outer diameter D1 at the location of the clamping area and a second outer diameter D2 at the location of the retaining radial projections, the first outer diameter D1 being smaller than the second outer diameter D2, the first outer diameter D1 and the diameter D3 of the maximum radial size being smaller than or equal to the inner diameter D0, and the second outer diameter D2 being larger than or equal to the inner diameter D0, - the collar or the connector is moved in order to leave the temporary accommodation space with regard to the collar and position the crimping collar around at least part of the front end of the hose and substantially opposite the clamping area of the connector, and - the collar is crimped for fixing the open front end of the flexible hose to the connector,