Assembly for implanting an acetabular cup in a cotyloïd cavity, comprising: - an acetabular cup, intended to be implanted in a cotyloïd cavity of a patient's pelvis, and - a gripping/impacting instrument for the acetabular cup, comprising: - a gripper, having an appropriate surface to come into contact with the acetabular cup, and equipped with reversible retaining members for retaining the acetabular cup, and - a gripping/impacting handle, - the gripper being a subassembly separated from the handle and capable to be assembled to said handle, comprising means (6, 7) for connecting to the handle; - the handle being a subassembly separated from the gripper and capable to be assembled to the gripper, comprising connecting means (17, 25, 26, 27, 30, 31) for connecting to the gripper, capable to cooperate with the connecting means comprised by the gripper to connect said handle to said gripper; - the reversible retaining members being in the form of snapping teeth suitable for engaging with a snapping rim comprised by the acetabular cup and for releasing the acetabular cup following a thrust exerted on the acetabular cup substantially along the axis of revolution of that acetabular cup, characterized in that: - the acetabular cup has at least two snapping rims; - the gripper comprises a mobile pusher, movable from a withdrawn position not hindering the assembly of the acetabular cup to the gripper, toward an extension position, this pusher exerting, during this movement, thrust on the acetabular cup substantially along the axis of revolution of said acetabular cup, so as to disengage the snapping rims comprised by the acetabular cup from their engagement with the snapping teeth comprised by the gripper; and - the assembly comprises means for actuating the moving pusher, making it possible to move that pusher from said withdrawn position to said extension position. - an acetabular cup, intended to be implanted in a cotyloïd cavity of a patient's pelvis, and - a gripping/impacting instrument for the acetabular cup, comprising: - a gripper, having an appropriate surface to come into contact with the acetabular cup, and equipped with reversible retaining members for retaining the acetabular cup, and - a gripping/impacting handle, - a gripper, having an appropriate surface to come into contact with the acetabular cup, and equipped with reversible retaining members for retaining the acetabular cup, and - a gripping/impacting handle, - the gripper being a subassembly separated from the handle and capable to be assembled to said handle, comprising means (6, 7) for connecting to the handle; - the handle being a subassembly separated from the gripper and capable to be assembled to the gripper, comprising connecting means (17, 25, 26, 27, 30, 31) for connecting to the gripper, capable to cooperate with the connecting means comprised by the gripper to connect said handle to said gripper; - the reversible retaining members being in the form of snapping teeth suitable for engaging with a snapping rim comprised by the acetabular cup and for releasing the acetabular cup following a thrust exerted on the acetabular cup substantially along the axis of revolution of that acetabular cup, characterized in that: - the acetabular cup has at least two snapping rims; - the gripper comprises a mobile pusher, movable from a withdrawn position not hindering the assembly of the acetabular cup to the gripper, toward an extension position, this pusher exerting, during this movement, thrust on the acetabular cup substantially along the axis of revolution of said acetabular cup, so as to disengage the snapping rims comprised by the acetabular cup from their engagement with the snapping teeth comprised by the gripper; and - the assembly comprises means for actuating the moving pusher, making it possible to move that pusher from said withdrawn position to said extension position.