The one‐dimensional stability of detonation waves characterized by one‐step irreversible Arrhenius kinetics is examined. The description of the steady structure in the limit of infinite activation energy is well known, and an examination is made of the linear unsteady perturbation equations in the same limit. The spectrum contains both a single real positive eigenvalue that vanishes in the limit and an infinite number of nonvanishing eigenvalues that define a growth rate which is an increasing function of frequency. Plausible qualitative extrapolation to finite activation energies provides an explanation of experimental results obtained by Alpert and Toong [Astronaut. Acta17, 539 (1972)].