To facilitate the laying work of supply pipes by means of a durable and useful connection structure therefor, which may be produced at lower costs.

A connection structure for supply pipes comprises a relay pipe 3 which has a flange 3b and a diameter-expanded portion 3c and is adapted to be fitted into the tip of a supply pipe 2 for a combination faucet, a check valve socket 4 which has one end of outside diameters to permit its insertion into the diameter-expanded portion 3c and provided with O rings 4d and a flange 4e on the outer periphery and which has the other end adapted to be coupled to a stopcock, and a clip 6 for bringing the flanges 3b and 4e into contact with each other while the one end of the check valve socket 4 is inserted into the relay pipe 3.