In a glassware forming machine, an actuating assembly of an operative member has a tubular connecting body; a shaft for supporting the operative member coupled to the connecting frame to translate and rotate about a fixed axis thereof; a pneumatic jack for displacing the supporting shaft along the axis; a cam and tappet device for rotating the supporting shaft in opposite directions about the axis and having a chamber and a cam and tappet assembly housed in the chamber and lubricated by a lubricating liquid contained in the chamber; and a hydraulic device for stabilizing the motion of the shaft; the chamber and the hydraulic stabilizing device constituting part of a single closed hydraulic circuit for feeding a common lubricating and operative liquid to the cam and tappet device and to the hydraulic stabilizing device.