Abstract: The invention provides a rotary-vane machine having a stationary shell including a casing member (2), a camming ring (4) having an internal, noncircular camming surface (6), and a flange member (8); a rotor (10) including at least two first vanes (12) fixedly attached to, or integral with, the rotor (10), a first cover plate (14) fixedly attachable to the rotor (10); a second cover plate (16) fixedly attachable to the rotor and integral with a first shaft (22) supported on its free end by bearing (26) mounted in the casing (2), and being provided with at least four ports (a) for access or egress of a working medium; a second shaft (23) supported by a first bearing (28) accommodated in the first cover plate (14) and by a second bearing (30) accommodated in the second cover plate (16); at least two second vanes (38) fixedly attached to the second shaft (23) and oscillatably accommodated within the rotor (10), and defining, together with the rotor (10), the first vanes (12) and the first and second cover plates