We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes (RNS) model, and the simpler Zeldovich-von Neumann-Doring (ZND) and Chapman-Jouguet (CJ) models. The determinants are functions of frequencies (‚;·), where ‚ is a complex variable dual to the time variable, and · 2 R di1 is dual to the transverse spatial variables. The zeros of these determinants in 0 correspond to perturbations that grow exponentially with time. The CJ determinant, ¢CJ(‚;·), turns out to be explicitly computable. The RNS and ZND determinants are impossible to compute explicitly, but we are able to compute their first-order low-frequency expansions with an error term that is uniformly small with re- spect to all possible (‚;·) directions. Somewhat surprisingly, this computation yields an Equivalence Theorem: the leading coecient in the expansions of both the RNS and ZND determinants is a constant multiple of ¢CJ! In this sense the low-frequency stability condi- tions for strong detonations in all three models are equivalent. By computing ¢CJ we are able to give low-frequency stability criteria valid for all three models in terms of the physical quantities: Mach number, Gruneisen coecient, compression ratio, and heat release. The Equivalence Theorem and its surrounding analysis is a step toward the rigorous theoretical justification of the CJ and ZND models as approximations to the full RNS model.