A general theory is developed for obtaining the tangential and normal derivatives of thermodynamic and kinematic properties just downstream of a curved, unsteady shock wave. The flow upstream of the shock need not be steady or uniform and the gas need not be thermally or calorically perfect. Because of the complexity of the results, explicit formulas are provided for the above derivatives when the flow is steady and two‐dimensional or axisymmetric, and the gas is perfect.