The chemical evolution of a hot gas subject to initial non-uniformities in velocity, pressure, temperature and reactant mass concentration is studied for moderate activation energies. It is demonstrated that such initial non-uniformities generate gradients in the distribution of chemical ignition times for each fluid particle, resulting in the creation of a high-speed, shockless reaction wave. If these gradients are sufficiently large, a transition from the high speed reaction wave to a strong detonation occurs. Time-dependent generalizations of the spontaneous flame concept, where the evolution of each fluid particle is determined by integration along particle paths only, are derived for initial velocity and pressure disturbances under the assumption of slowly varying initial disturbances. The unsteady structure of the high-speed reaction wave arising due to reaction from initial non-uniformities is investigated for the moderate activation energy used.