A rotary piston machine of displacement type, comprising two mutually continuously movable parts (101, 102) having co-axial rotation axes (155) and mutually variable movement, wherein the first part (102) internally has at least two radially inwardly directed wings (139) with mutual angular distance along the curved inside wall (150) of the part between the wings (139), wherein the second part (101) has a hub (146) which has at least two radially outwardly directed wings (147) with mutual angular distance, wherein a portion of the hub (146) between the wings of the second part is in slidable or adjacent contact with a curved, free end portion (157) of the wings on the first part (102), wherein a curved, free end portion (158) of each wing on the other part (101) is in slidable or adjacent contact with the curved inside wall (150) on the first part (102) which is located between respective ones of two neighbouring wings (139) on the first part (102), wherein the wings (147) of the second part (101) being movable between respective neighbouring wings (139) on the first part, so that chambers which are created between co-operative pairs of wings on the first part and the second part successively increase and decrease, and decrease and increase, respectively, in volume during the course of a rotation cycle of the created chambers, and wherein movements of said mutually movable parts are caused by a controlling gear arrangement (201) which operationally co-operates with a rotatable main drive shaft (116) of the machine.