A machine for conveying containers, comprising: a guide extending along an advancement direction of the containers; a main carriage slidably mounted on said guide , said guide and said main carriage together defining a main linear motor; at least one auxiliary carriage slidably mounted on said guide , said guide and said auxiliary carriage together defining an auxiliary linear motor; a pressing device mounted on said main carriage and movable along an axis coinciding with the main axis of the container between a raised rest position, in which the pressing device and the container are not in contact, and a lowered constrained position in which the pressing device applies a pressing force on the top of a container; a control unit electrically connected to said guide and configured for controlling the sliding of said main carriage and said auxiliary carriage on said guide and a mutual distance thereof; actuating means operatively connected to said pressing device and configured for moving said pressing device between said raised rest position and said lowered constrained position; said actuating means being operatively interposed between said pressing device and said auxiliary carriage , and being activatable following the variation of the mutual distance between said main carriage and said auxiliary carriage ; said control unit being configured for commanding the variation of the mutual distance between the main carriage and the auxiliary carriage so as to activate said actuating means ; wherein the pressing device is rotationally independent of the axial movement between the raised rest position and the lowered constrained position. a guide extending along an advancement direction of the containers; a main carriage slidably mounted on said guide , said guide and said main carriage together defining a main linear motor; at least one auxiliary carriage slidably mounted on said guide , said guide and said auxiliary carriage together defining an auxiliary linear motor; a pressing device mounted on said main carriage and movable along an axis coinciding with the main axis of the container between a raised rest position, in which the pressing device and the container are not in contact, and a lowered constrained position in which the pressing device applies a pressing force on the top of a container; a control unit electrically connected to said guide and configured for controlling the sliding of said main carriage and said auxiliary carriage on said guide and a mutual distance thereof; actuating means operatively connected to said pressing device and configured for moving said pressing device between said raised rest position and said lowered constrained position; said actuating means being operatively interposed between said pressing device and said auxiliary carriage , and being activatable following the variation of the mutual distance between said main carriage and said auxiliary carriage ; said control unit being configured for commanding the variation of the mutual distance between the main carriage and the auxiliary carriage so as to activate said actuating means ; wherein the pressing device is rotationally independent of the axial movement between the raised rest position and the lowered constrained position. <EOS>