Abstract: This invention relates to flexible high-pressure hoses of the kind having a wall made of elastomeric material which is strengthened by a stress-resistant reinforcement which is embedded in the wall and which is formed by at least two superimposed layers of cables inclined in opposite directions, with, at one end, an obturating or connecting device comprising a spigot which is inserted in the hose and an external clamping collar, the spigot and the collar having, on their adjacent surfaces, a channel in the one case and a corresponding ridge in the other.According to the invention, the channel and the ridge each have parallel clamping surfaces which are inclined in opposite directions and their radial height is substantially equal to or slightly greater than the thickness of the wall of the hose so that, in the state where the device is assembled to the hose, the crest of the ridge at least partly enters the channel.