—We examine unstable overdriven detonations with one-step Arrhenius' kinetics in the limit of infinite activation energy. For the one-dimensional problem we show how a ccrtain class of initial disturbances lead to thermal runaway for the entire detonation structure, with thc shock temperature and pressure increasing several-fold in an extremely small time interval. This behavior resembles the sharp transients reported by others in numerical computations. For the two-dimensional problem, run-away occurs at discrete points distributed along the plane of the shock with spacing determined by the initial disturbance. This description is characterized by very large transverse pressure gradients which, in turn, will give rise to the transverse shock waves that are a familiar feature of unstable multidimensional detonations.