An orbital engine with a first outer generally tubular body with a first axis, and a second generally tubular inner orbiter body with a second axis, the second inner body being moveable within the first outer body. The first and second axes are parallel, but not colinear. The second inner body revolves, but does not rotate, within the first outer body Vanes extending generally radially relative to both the inner and outer bodies define multiple chambers in the space between the outside of the inner body and the inside of the outer body. The vanes reciprocate relative to both the inner and outer bodies, and no vane traverses the entire inner surface of the outer body. When fitted with ports in the outer body and valves, the orbital engine may be implemented as an internal combustion engine, gas compressor, liquid pump, air motor, blower, fan or turbine, etc.