Clamp (1) for holding a container (2) by a neck (3) in a container handling machine, said clamp (1) comprising a pair of resilient arms (5) and a pair of neck grippers (7) provided at respective ends (6) of the arms (5), said arms (5) and said neck grippers (7) being configured to allow the container neck (3) to be laterally engaged between the neck grippers (7), each neck gripper (7) being pivotally mounted on the corresponding arm (5) about a rotation axis (8), and having at least two gripping jaws (9a, 9b) of different dimensions, configured to cooperate with container necks (3a, 3b) of different sizes.