A machine for processing containers, comprising a conveying device and at least one processing unit coupled to the conveying device to be carried along a processing path; the processing unit including: a winding element, having an outer lateral surface designed to receive, and cause winding of, a portion of labelling material in a tubular configuration with opposite ends overlapped, and a top surface designed to support a bottom portion of a container to be processed; a sealing device including a sealing element having a functional surface adapted to cooperate with said portion wound about said winding body for performing a welding process of the overlapped ends, as the processing unit is carried along said path, to form a sleeve label; and an electrically-controlled displacement device, operable to cause a relative displacement between said sleeve label and said container, thereby the sleeve label is placed about a desired portion of the container, characterized in that the processing unit further comprises a control circuit, coupled to the sealing device and the displacement device and configured to jointly control operation thereof, wherein the control circuit includes the following modules, which are conveniently all integrated in a same printed circuit board 60' within case 61: a control module; a first driving module, configured to provide a first driving signal (EV 1) to an actuator element of the sealing device, to cause displacement of the sealing element towards, and from, the portion of labelling material; a second driving module, configured to provide a second driving signal (EV 2) to a respective actuator element of the displacement device, to cause relative displacement of the sleeve label with respect to the container; and an interface module, configured to receive control signals (S c) from a supervising unit of the processing machine. a winding element, having an outer lateral surface designed to receive, and cause winding of, a portion of labelling material in a tubular configuration with opposite ends overlapped, and a top surface designed to support a bottom portion of a container to be processed; a sealing device including a sealing element having a functional surface adapted to cooperate with said portion wound about said winding body for performing a welding process of the overlapped ends, as the processing unit is carried along said path, to form a sleeve label; and an electrically-controlled displacement device, operable to cause a relative displacement between said sleeve label and said container, thereby the sleeve label is placed about a desired portion of the container, characterized in that the processing unit further comprises a control circuit, coupled to the sealing device and the displacement device and configured to jointly control operation thereof, wherein the control circuit includes the following modules, which are conveniently all integrated in a same printed circuit board 60' within case 61: a control module; a first driving module, configured to provide a first driving signal (EV 1) to an actuator element of the sealing device, to cause displacement of the sealing element towards, and from, the portion of labelling material; a second driving module, configured to provide a second driving signal (EV 2) to a respective actuator element of the displacement device, to cause relative displacement of the sleeve label with respect to the container; and an interface module, configured to receive control signals (S c) from a supervising unit of the processing machine. a control module; a first driving module, configured to provide a first driving signal (EV 1) to an actuator element of the sealing device, to cause displacement of the sealing element towards, and from, the portion of labelling material; a second driving module, configured to provide a second driving signal (EV 2) to a respective actuator element of the displacement device, to cause relative displacement of the sleeve label with respect to the container; and an interface module, configured to receive control signals (S c) from a supervising unit of the processing machine.