A gripper device for gripping the neck of a hollow body from the outside, which gripper device includes an annular body supporting at least two gripper parts each having its own bearing face, said gripper parts being movable substantially radially and constrained by an elastic device in such a way that the gripper parts are able to occupy a first radial position in which they bear against a buffer of the annular body with their bearing face projecting into the annular body, and a second radial position in which they are pushed back with their bearing face bearing against the exterior wall of the neck of a hollow body engaged in the annular body. The bearing faces of the gripper parts are bowed in the overall shape of an arc of a cylinder.