Sealing in rotary positive displacement machines based on trochoidal geometry that comprise a helical rotor that undergoes planetary motion within a helical stator is described. Seals can be mounted on the rotor, the stator, or both. The rotor can have a hypotrochoidal cross-section, with the corresponding stator cavity profile being the outer envelope of the rotor as it undergoes planetary motion, or the stator cavity can have an epitrochoidal cross-section with the corresponding rotor profile being the inner envelope of the trochoid as it undergoes planetary motion. In some embodiments, the geometry is offset in a manner that provides advantages with respect to sealing in the rotary machine. In multi-stage embodiments, the rotor-stator geometry remains substantially constant or varies along the axis of the rotary machine.