Abstract: Rotary machines of the type having a fluid chamber of changing volume, e.g. as ion an engine or pump, in which two rotors rotate in the same direction; a cylindrical surface of the first rotor of substantial arcuate extent, of radius substantially equal to the radius of its bore is arranged for sealing relationship throughout a chamber-defining range of rotation, with both its bore wall and with a surface of the second rotor; and the surface of the second rotor has a progressively changing radius to cause the chamber volume to progressively change during rotation. For forming multiple chambers, each subject to successive compression and expansion, each of the rotors has a transition surface preceding its large cylindrical surface and a transition surface following its large cylindrical surface, with an apex seal formed at each end of each large cylindrical surface.