The present invention provides a quick connector for establishing a snapping connection between a tubular male part (50) and a female part (40) of a fluid connection system. The connector has retaining means (10) adapted to be set within the mouth portion (41) of the female part (40) and having a resilient member (20) for snapping engagement with both a thickened portion (52) of the male part (50) and an annular groove (42) in the mouth portion (41) of the female part (40) when the resilient member (20), which is held by the retaining means (10) in an axially fixed position, is stretched in the radial direction due to the snapping engagement with the male part (50).