A rotating externally mounted positive displacement pump having at least two displacing bodies which are driven synchronously with respect to one another and are fastened on the end side on associated shafts, the shafts being mounted in each case by way of a first, radially acting bearing and a second, radially and axially acting bearing, and the shafts being coupled to one another by way of a synchronizing gear mechanism, is developed in that the bearings are fitted into seat bores of a housing which is manufactured in one piece, and in that the synchronizing gear mechanism is arranged between the respective bearings.