Device for the connection of a duct including a tubular body provided with an axial stop for a cylindrical sleeve that defines a tubular accommodating housing and has an end which delimits an annular inlet to the housing that is radially deformable elastically. The housing includes a maintaining member for maintaining the end of the sleeve in a deformed state, the member being designed to be movable between an active position in which it maintains the end in the deformed state and an inactive position in which it is carried by the duct during the introduction thereof and allows the end to return to its rest state.