Positive displacement machine such as a compressor, expander, pump or the like, for displacing a gaseous or liquid medium, the machine containing an element with at least one inlet and at least one outlet for the medium and at least two cooperating driven moving parts. The mutual periodic movement of the moving parts displaces the medium from the inlet to the outlet. Each of the at least two driven cooperating moving parts is provided with its own individual drive. The element is provided with a kinematic synchronisation coupling between the at least two cooperating moving parts for the mutual kinematic synchronisation of their movements.