The supersonic flight of a slender projectile in a fluid which may undergo internal non-equilibrium transformations is examined by a systematic perturbation scheme. In the frozen limit, the classical results of Whitham and his celebrated ‘rule’ are recovered. Unlike the classical theory, however, the shape of the nose shock can be expressed explicitly in terms of known functions when the relaxation decay length becomes of the same order as a characteristic length scale. The theoretically predicted shock angle, expressed as a function of the radial distance, is found to be in excellent agreement with the experimental measurements of Wegener and Klikoff.