Abstract: A machine, in particular a working machine for the compression and conveyance of fluids, comprises a cylinder (2) and a thin-walled annular piston (4) arranged eccentrically with respect to the cylinder (2), with the piston being in flat contact either inside or outside with a cylinder wall (8). The cylinder (2) or the cylinder housing, contains a parting element (12) whereby a suction chamber (33) is separated from a pressure chamber (35) between the cylinder and the annular piston (4) and whereby by means of a rotating body a rotating motion may be imparted to the annular piston (4). The annular piston (4) is to be exposed to low alternating stresses and between the cylinder (2) and the annular piston (4) a low local surface pressure is to be achieved, while assuring a reliable contact in the rolling range (A).