A rotary vortex machine comprising a stator (1) with an internal annular space (4) accommodating vanes (9), an inlet passage (2) and an outlet passage (3) for a service fluid, and a fluid energy converting stage installed in the stator (1) on a drive shaft (5) and comprising a rotor (6) having an external annular space (7) combined with the annular space (4) of the stator (1) and forming, together with said annular space (4), a working annular chamber (8), and a bridge (10) disposed in the annular space (7) of the rotor (6) and dividing said annular space (7) of the rotor into suction and delivery volumes communicating with the inlet passage (2) and the outlet passage (3) of the stator (1), said rotor (6) having a curvilinear inlet passage (11) and a curvilinear outlet passage (12) which connect the suction and delivery volumes of the annular space (7) of the rotor (6) with the inlet passage (2) and the outlet passage (3) of the stator (1), said curvilinear inlet and outlet passages being arranged on both sides of the bridge (10) in such a manner that the flow of the service fluid moves through said curvilinear passages (11, 12), essentially, in one and the same direction, the bridge (10) in the zone of said curvilinear passages (11, 12) having a variable cross section and being positioned at an angle relative to a radial plane passing through said bridge (10).