The invention relates to a positive displacement pump 1 for conveying medical fluids, which pump has a pumping chamber 5 and a positive displacement element 15, and to a blood treatment apparatus comprising a positive displacement pump 1. In addition, the invention relates to a method for controlling a positive displacement pump 1 for conveying medical fluids. The positive displacement pump 1 according to the invention has an actuation member 20 in operative connection with the positive displacement element 20 for displacing or deforming the positive displacement element in order to convey the fluid into the pumping chamber or out of the pumping chamber, and a drive device 21 for displacing the actuation member 20. A control unit 14 is provided for to controlling the drive device 21 and an inlet valve 12 and outlet valve 13. The actuation member 20 is in operative connection with the positive displacement element 15 via a working chamber 19 that is filled with gas and has a sealed volume. In order to achieve a high conveying precision, the pressure in the working chamber 5 is kept constant when the positive displacement element 15 is moved.