This invention refers to a hydraulic or pneumatic machine with tilting blades, running either as an engine on a fluid flow or on pressure fluid or as a pump or a compressor. The hydraulic or pneumatic machine on a fluid flow according to the invention consists of a cylindrical casing with inlet and outlet openings, radially arranged, diametrically oposed, along the fluid flowing direction, some disk like rotors with tilting blades, hinged over their front faces and provided with driving mechanisms of their own, and some fixed drums located between the rotors, concentrically to them, making inside the machine some channels, symetrically arranged on one or several stages. Flowing through the channels, the fluid drives the tilting blades causing the movement of the rotors, all the rotors moving to one sense being coupled to the same outlet shaft of the machine. The tilting blades of the hydraulic or pneumatic machine operating according to the invention with pressure fluid, run in variable depth grooves located in the rings between the front faces of the rotors and connected to the fluid circuit, the operation conditions of the machine-motor or pump-being determined by the moving sense of the blade in the groove.