A capping system for closing a container using a metallic cap comprising: - a capping head for closing a container using a metallic cap, having: o a hollow main body which extends about a longitudinal axis of the capping head, o a plurality of capping ends, integral with the main body and positioned below the main body relative to a direction of vertical extension, having a capping profile (4, 5) on their inner face facing towards the longitudinal axis, o a capping ring, positioned outside the main body, movable vertically along the direction of said longitudinal axis and configured for elastically deforming the plurality of capping ends by a relative translation along the longitudinal axis, at least one pair of capping ends has a change of the capping profile between a concave capping profile and a convex capping profile; - a device for retaining the cap on a neck of the container, positioned inside the capping head and comprising a first spring operatively connected to a first contact piston, movable along the longitudinal axis of the capping head; - an inner casing configured to contain inside it at least a part of the capping head, comprising a lateral surface, an upper surface extending in a direction transversal to the longitudinal axis of the capping head; - a contact ring, positioned below the inner casing along the longitudinal axis in a direction of vertical extension and configured to contain inside it at least a part of the capping head; - an outer casing, comprising an outer surface and a contact surface extending in a direction transversal to the longitudinal axis of the capping head, configured to contain inside it the inner casing and the contact ring; - an actuator operatively connected to the outer casing for moving, and exerting a force on, said outer casing along the longitudinal axis in the opposite direction relative to the vertical direction of extension, the system being characterized in that it further comprises: - a second spring, contained inside the outer casing outside the inner casing, interposed between the upper surface and the contact surface and acting between said upper surface and said contact surface; - a third spring, contained inside the outer casing outside the inner casing, interposed between the contact surface and the contact ring and acting between said contact surface and said contact ring to apply a downward thrust to the contact ring which is transferred to the capping ring coming into contact with a bottom of the contact ring. - a capping head for closing a container using a metallic cap, having: o a hollow main body which extends about a longitudinal axis of the capping head, o a plurality of capping ends, integral with the main body and positioned below the main body relative to a direction of vertical extension, having a capping profile (4, 5) on their inner face facing towards the longitudinal axis, o a capping ring, positioned outside the main body, movable vertically along the direction of said longitudinal axis and configured for elastically deforming the plurality of capping ends by a relative translation along the longitudinal axis, at least one pair of capping ends has a change of the capping profile between a concave capping profile and a convex capping profile; o a hollow main body which extends about a longitudinal axis of the capping head, o a plurality of capping ends, integral with the main body and positioned below the main body relative to a direction of vertical extension, having a capping profile (4, 5) on their inner face facing towards the longitudinal axis, o a capping ring, positioned outside the main body, movable vertically along the direction of said longitudinal axis and configured for elastically deforming the plurality of capping ends by a relative translation along the longitudinal axis, at least one pair of capping ends has a change of the capping profile between a concave capping profile and a convex capping profile; - a device for retaining the cap on a neck of the container, positioned inside the capping head and comprising a first spring operatively connected to a first contact piston, movable along the longitudinal axis of the capping head; - an inner casing configured to contain inside it at least a part of the capping head, comprising a lateral surface, an upper surface extending in a direction transversal to the longitudinal axis of the capping head; - a contact ring, positioned below the inner casing along the longitudinal axis in a direction of vertical extension and configured to contain inside it at least a part of the capping head; - an outer casing, comprising an outer surface and a contact surface extending in a direction transversal to the longitudinal axis of the capping head, configured to contain inside it the inner casing and the contact ring; - an actuator operatively connected to the outer casing for moving, and exerting a force on, said outer casing along the longitudinal axis in the opposite direction relative to the vertical direction of extension, the system being characterized in that it further comprises: - a second spring, contained inside the outer casing outside the inner casing, interposed between the upper surface and the contact surface and acting between said upper surface and said contact surface; - a third spring, contained inside the outer casing outside the inner casing, interposed between the contact surface and the contact ring and acting between said contact surface and said contact ring to apply a downward thrust to the contact ring which is transferred to the capping ring coming into contact with a bottom of the contact ring.