Abstract: The rotary machine, for example an air pump, has two rotors and vanes carried by the rotors within a housing, to pump fluid between an inlet and an outlet on opposite sides of the housing. The vanes are guided by tracks, so that the vanes are withdrawn flush with the rotor surfaces at a contact line between the rotors. In one embodiment, ends of the vanes are carried in carriers by means of bearing blocks. The carriers rotate at an average speed equal to that of the rotors, to reduce the movement of the ends of the vanes. The mechanism can be employed in a single rotor machine.