Abstract: A rotary machine for a compression or an expansion of a gaseous working fluid comprises a machine housing (10), a rotor (11) which is rotatably mounted within said housing and which, in its peripheral outer surface, is provided with at least one helically extending groove (14), having a depth varying along its length and serving as a flow passage for the working fluid, and a rotatable separation wheel (15) which is provided with a number of blades (17), evenly distributed in the circumferential direction of said wheel and serving as separation elements, successively insertable into the groove (14) of the rotor (11) and arranged to divide the groove (14) into a number of working chambers which follow one after the other in the longitudinal direction of the groove and which, during coordinated simultaneous rotation of the rotor (11) and the separation wheel (15), are brought to move along the groove (14) in the longitudinal direction thereof while successively changing their volume.