  We establish one-dimensional spectral, or "normal modes", stability of ZND
detonations in the small heat release limit and the related high overdrive
limit with heat release and activation energy held fixed, verifying numerical
observations of Erpenbeck in the 1960s. The key technical points are a
strategic rescaling of parameters converting the infinite overdrive limit to a
finite, regular perturbation problem, and a careful high-frequency analysis
depending uniformly on model parameters. The latter recovers the important
result of high-frequency stability established by Erpenbeck by somewhat
different techniques. Notably, the techniques used here yield quantitative
estimates well suited for numerical stability investigation.
