Theory is presented for oblique shock waves involving (1) heat exchange,k1, (2) transfer of part of the compressible fluid,k2, to an incompressible state, and (3) change in specific heat ratios,k3. By matching mass flow, momentum, and energy relations across an oblique finite disturbance it is shown that these additional conditions introduce new terms in the solution of the formkiu1/(u1−u2). Forkinot zero a minimum shock angle is found which always exceeds the Mach angle by a definite increment. For air‐flow atu1/a* of 1.5 with dew point −20°F this increment is calculated as 3.1 degrees. For expansion about a corner such flow differs from the Prandl‐Meyer type and in supersonic nozzles, for example, oblique shock waves are predicted which can explain anomalous pressure losses, the presence of extraneous waves, and non‐isentropic effects. Hodographs of the velocity solution include a triply infinite set of curves, one, the usual set, introduced by Mach number as parameter and the other two byki. The theory includes physically possible normal and oblique flows involving increase of supersonic velocities and subsonic velocities of which oblique flame fronts are indicated as one form. Applied to air condensations in hypersonic flows isentropic disturbances having appreciable angular flow shift and stagnation pressure losses are predicted.