Abstract: This paper derives a series of flow and performance parametric relations for supersonic and transonic turbine stages, using nondimensional nozzle vane exit speed i and rotor speed ui as independent variables. These formulas are applicable to elementary stages or to the whole stage repre sented at characteristic radii. Illustrative curves are given with one set of selected parameters.In addition, the recent developments of transonic and supersonic turbine research over the world are briefly reviewed, with the roles of various stages marked on an efficiency versus pressure ratio diagram.