Closure device for a container of a liquid to pasty product, said closure device comprising: - a closure base comprising a closure wall having a through communication conduit, said closure wall being intended to close the opening of a container of a liquid to pasty product, - a stopper movable in the communication conduit between a closed position and an open position, wherein the stopper comprises a bottom and a cavity open on one side of the closure wall and closed by said bottom, the cavity comprising at least one lateral opening, the stopper being arranged with the communication conduit so that: - in the closed position, said bottom sealingly closes the communication conduit, and - in the open position, the stopper is partially out of the communication conduit, said lateral opening(s) and said bottom being out of the communication conduit, so that the communication conduit is open in fluid communication through the stopper, the stopper comprising a thrust surface on the edges of the said cavity capable of receiving in axial abutment the edges of a first opening of a tube belonging to a dispensing device in the direction of opening of the stopper, wherein the closure wall comprises a cone flaring out from the opening of the communication conduit on a first surface of the closure wall, the bottom as well as said lateral opening(s) of the closure being housed in this cone and at a distance from the walls of this cone when the closure is in the open position. - a closure base comprising a closure wall having a through communication conduit, said closure wall being intended to close the opening of a container of a liquid to pasty product, - a stopper movable in the communication conduit between a closed position and an open position, wherein the stopper comprises a bottom and a cavity open on one side of the closure wall and closed by said bottom, the cavity comprising at least one lateral opening, the stopper being arranged with the communication conduit so that: - in the closed position, said bottom sealingly closes the communication conduit, and - in the open position, the stopper is partially out of the communication conduit, said lateral opening(s) and said bottom being out of the communication conduit, so that the communication conduit is open in fluid communication through the stopper, - in the closed position, said bottom sealingly closes the communication conduit, and - in the open position, the stopper is partially out of the communication conduit, said lateral opening(s) and said bottom being out of the communication conduit, so that the communication conduit is open in fluid communication through the stopper, the stopper comprising a thrust surface on the edges of the said cavity capable of receiving in axial abutment the edges of a first opening of a tube belonging to a dispensing device in the direction of opening of the stopper, wherein the closure wall comprises a cone flaring out from the opening of the communication conduit on a first surface of the closure wall, the bottom as well as said lateral opening(s) of the closure being housed in this cone and at a distance from the walls of this cone when the closure is in the open position.