A rotary power device of the swinging piston type has a cylindrical rotor mounted between internal and external portions of a stator. The internal stator provides intake and exhaust channels and may hold an igniter. The external stator includes two axially adjacent cam tracks with diametrically opposed eccentricities with respect to the axis of rotation. The rotor includes two axially spaced sets of sector-shaped compartments arranged at equal angular intervals around the inner stator, where each set is axially aligned with a respective cam track. Each compartment is open at the periphery of the rotor and has an inner opening aligned with ports in the internal stator. A sector-shaped piston mounted in each compartment pivots about an axis at one vertex of the compartment. Each piston includes a roller follower for engaging the respective cam track as the rotor rotates. The rotary power device may be configured as a two-phase internal combustion engine, a compressor, a motor-driven pump, a fluid-driven pump or compressor, or a hydraulic motor by modifying the central internal stator.