A capping device for capping containers filled with a pourable product, the capping device (6, 6') comprising: - a support member for supporting at least one container to be capped by at least one cap; - a tubular sleeve having a longitudinal axis, a first axial opening facing the support member and a second axial opening opposite the first axial opening; and - a capping head extending along said longitudinal axis and slidably engaging the second axial opening of the sleeve thereby closing said second axial opening; the capping head comprising a capping portion with a seat for receiving and retaining the cap, the capping portion being arranged within the sleeve and being axially movable through the sleeve for applying said cap to the supported container; wherein the sleeve is axially movable towards and away from the support member and between: - a first position, in which the first axial opening is open and axially spaced from the support member; and - a second position, in which the sleeve cooperates in contact with the support member or with the container for closing the first axial opening and thereby delimiting a pressurization chamber, which chamber is configured to be pressurized for pressurizing an inner environment of said supported container; wherein the capping head comprises a control rod extending along said longitudinal axis, axially movable towards and away from said support member, carrying at one end portion thereof said capping portion and engaging in a sliding manner said second axial opening substantially in a fluid-tight manner so as to delimit, together with said sleeve, said pressurization chamber open at said first axial opening and closable substantially in a fluid-tight manner by the sleeve being in said second position; characterized in that the capping portion radially extends up to an internal lateral wall of the sleeve and is axially movable towards and away from the support member in sliding contact with said internal wall to define a piston within the sleeve; and wherein the device is configured so that the capping portion applies the cap to the container by means of an axial capping movement towards the support member; and wherein the device is configured so that the capping portion pressurizes the chamber by means of the same axial capping movement. - a support member for supporting at least one container to be capped by at least one cap; - a tubular sleeve having a longitudinal axis, a first axial opening facing the support member and a second axial opening opposite the first axial opening; and - a capping head extending along said longitudinal axis and slidably engaging the second axial opening of the sleeve thereby closing said second axial opening; the capping head comprising a capping portion with a seat for receiving and retaining the cap, the capping portion being arranged within the sleeve and being axially movable through the sleeve for applying said cap to the supported container; wherein the sleeve is axially movable towards and away from the support member and between: - a first position, in which the first axial opening is open and axially spaced from the support member; and - a second position, in which the sleeve cooperates in contact with the support member or with the container for closing the first axial opening and thereby delimiting a pressurization chamber, which chamber is configured to be pressurized for pressurizing an inner environment of said supported container; - a first position, in which the first axial opening is open and axially spaced from the support member; and - a second position, in which the sleeve cooperates in contact with the support member or with the container for closing the first axial opening and thereby delimiting a pressurization chamber, which chamber is configured to be pressurized for pressurizing an inner environment of said supported container; wherein the capping head comprises a control rod extending along said longitudinal axis, axially movable towards and away from said support member, carrying at one end portion thereof said capping portion and engaging in a sliding manner said second axial opening substantially in a fluid-tight manner so as to delimit, together with said sleeve, said pressurization chamber open at said first axial opening and closable substantially in a fluid-tight manner by the sleeve being in said second position; characterized in that the capping portion radially extends up to an internal lateral wall of the sleeve and is axially movable towards and away from the support member in sliding contact with said internal wall to define a piston within the sleeve; and wherein the device is configured so that the capping portion applies the cap to the container by means of an axial capping movement towards the support member; and wherein the device is configured so that the capping portion pressurizes the chamber by means of the same axial capping movement.