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The paper develops a description for the propagation of an unsupported, unsteady, multidimensional detonation wave for an explosive with a fully resolved reaction zone and a polytropic equation of state. The main features of the detonation are determined once the leading shock surface is known. The principal result is that the detonation velocity in the direction along the normal to the shock is the Chapman-Jouguet velocity plus a correction that is a function of the local total curvature of the shock. A specific example of unsteady propagation is discussed and the stability of a two-dimensional steady solution is examined.