of the stator elements 6 the upper housing part 2 secures the stator elements 6 around the shaft 4 and holds them in their predetermined position the described method of assembly of the stator elements 6 does not form part of the present invention and is adduced in order to clarify how a one piece housing part including both a vacuum chamber and pump active elements can be used in the housing part 3 in addition to bearing means 8 there is provided drive means 9 e g electrical coils which cooperate with permanent magnets arranged on the shaft 4 setting the shaft in rapid rotation the bearing means 8 can be formed as a ball bearing magnetic bearing or gas bearing the lower housing part 3 also includes a gas outlet channel 30 leading to a gas outlet union when the vacuum pump itself is not compressed to the atmospheric pressure a forevacuum pump is connected with this gas outlet union also are arranged in the upper housing part 2 a first vacuum chamber 20 and a second vacuum chamber 21 with a lower pressure being produced in the first vacuum chamber 20 than in the second vacuum chamber.