In order to investigate the influence of the non-steadiness of wave motion on the thickness of the detonation front, a 'quasi-steady' kinetic model of the induction process is considered and the flow field treated as that of a decaying blast wave. The 'quasi-steady' model is based on the assumption that the induction time is governed by the same law as that corresponding to steady flow conditions, while the thermodynamic parameters of state vary because of the non-steady nature of the blast wave. For a point, line or plane symmetrical motion, the induction period and the corresponding wave thickness, identified as the distance between the shock and the combustion front, have been expressed, under such circumstances, in terms of the Mach number at the moment when a given particle was overtaken by the front. The results demonstrate that in the non-steady case the wave thickness can become significantly larger than that corresponding to the same Mach number in steady flow, and that, in fact, as the initially overdriven wave decays, the induction time rapidly approaches infinity, indicating a complete extinction of the detonation process. The theory has been shown to be in satisfactory agreement with experimental observations of marginal detonation in a hydrogenoxygen system, and the point of extinction was found to occur there when the front velocity became roughly equal to the Chapman-Jouguet value.