The present invention relates to a quick connector especially for low-pressure fluid transfer, and a method of snap connection of a pipe to this connector quick connection. This connection (1) comprises: - a pipe (10) circumferentially bulging (11) for its snap connection at one end (21) of a connector (20); - This snap fitting which comprises a sleeve (20) of which a first and a second female ends (21 and 22) are respectively intended to be connected to this pipe and a tubular end, and a seal (24) adjacent to this first end mounted abutment radially between the sleeve and this pipe; and means (30) cooperating with this bulge and with slots (20a) formed in the socket for connecting the hose. According to the invention, these means comprise a shell (30) which is attached to the bulge and which snaps into the slots when connecting the pipe to the sleeve by being mounted adjacent to the seal, so that this shell blocks axially the pipe and the gasket in the socket.
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