Capping machine for capping containers, comprising: - a line to feed caps, - a line to transport said containers, - an apparatus comprising a plurality of transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H), mobile with continuous rotary motion around a main axis of rotation, and a main actuator configured to drive said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) in rotation around said main axis of rotation, said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) being configured to pick up caps individually fed by said feed line and to deposit each of them on a respective container to be capped and advancing on said transport line, wherein each transport unit (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) comprises a gripping head to grip the caps, the apparatus also comprising at least two movement groups (13; 14) each configured to move a first or second group of said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) according to an oscillating movement along a displacement directrix having at least one radial component with respect to said main axis of rotation, between a retracted condition, in which said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) are closer to the main axis of rotation, and an extended condition, in which said transport units (12A, 12C, 12E, 12G, 12B, 12D, 12F, 12H) are more distant from the main axis of rotation, each of said at least two movement groups (13; 14) comprising a plurality of articulated movement devices each moving a respective one of said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) according to an alternate movement between said retracted condition and said extended condition, in succession first into a pick-up position where the cap is picked up, and subsequently into a delivery position where the cap is delivered onto a respective container; wherein the pick-up and delivery positions of a cap are located, with reference to said radial component, between said retracted condition and said extended condition; and wherein transport units (12A, 12C, 12E, 12G) comprised in said first group are disposed alternately with transport units (12B, 12D, 12F, 12H) comprised in said second group, so that two consecutive transport units (12A, 12C, 12E, 12G, 12B, 12D, 12F, 12H) are respectively constrained to a different movement group (13; 14), and - a programmable control and management unit, which is configured to control, in a coordinated manner, the movement of said apparatus with the movement of said feed line of the caps, and possibly with the movement of said transport line of the containers, the capping machine being characterized in that it comprises at least one detection device configured to detect the position and/or orientation of the caps on said feed line, and in that said apparatus comprises at least two motor members (28; 29) each configured to drive a respective one of said movement groups (13; 14) in order to move said articulated movement devices so as to take said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) in succession into said pick-up and delivery positions of the cap. - a line to feed caps, - a line to transport said containers, - an apparatus comprising a plurality of transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H), mobile with continuous rotary motion around a main axis of rotation, and a main actuator configured to drive said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) in rotation around said main axis of rotation, said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) being configured to pick up caps individually fed by said feed line and to deposit each of them on a respective container to be capped and advancing on said transport line, wherein each transport unit (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) comprises a gripping head to grip the caps, the apparatus also comprising at least two movement groups (13; 14) each configured to move a first or second group of said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) according to an oscillating movement along a displacement directrix having at least one radial component with respect to said main axis of rotation, between a retracted condition, in which said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) are closer to the main axis of rotation, and an extended condition, in which said transport units (12A, 12C, 12E, 12G, 12B, 12D, 12F, 12H) are more distant from the main axis of rotation, each of said at least two movement groups (13; 14) comprising a plurality of articulated movement devices each moving a respective one of said transport units (12A, 12C, 12E, 12G; 12B, 12D, 12F, 12H) according to an alternate movement between said retracted condition and said extended condition, in succession first into a pick-up position where the cap is picked up, and subsequently into a delivery position where the cap is delivered onto a respective container; wherein the pick-up and delivery positions of a cap are located, with reference to said radial component, between said retracted condition and said extended condition; and wherein transport units (12A, 12C, 12E, 12G) comprised in said first group are disposed alternately with transport units (12B, 12D, 12F, 12H) comprised in said second group, so that two consecutive transport units (12A, 12C, 12E, 12G, 12B, 12D, 12F, 12H) are respectively constrained to a different movement group (13; 14), and - a programmable control and management unit, which is configured to control, in a coordinated manner, the movement of said apparatus with the movement of said feed line of the caps, and possibly with the movement of said transport line of the containers,