An oscillating positive displacement pump with at least one mobile part arranged to be movable relative to a fixed part. The mobile part is driven and drives a displacement element of the positive displacement pump. An electrodynamic drive is provided as a drive, on which a plurality of coils and permanent magnets are provided that are arranged on the mobile part of the drive respectively, and at least one guide member is provided on the drive, which allows the mobile part to move only along a degree of translation freedom. The positive displacement pump is designed as a diaphragm pump, which is associated with a measurement and control unit with a data storage and data processor, which processes a position signal of the mobile part and the strength of the drive current as a measured and/or control variable. An arrangement of a plurality of such positive displacement pumps and a method of operating at least one such oscillating positive displacement pump are also provided.