In this paper, the detonation propensity of different compositions of mixtures of hydrogen, propane and methane with air has been evaluated over a wide range of compositions. We supplement the conventional calculations of the induction delay with calculations of the characteristic acceleration parameter recently suggested by Radulescu, Sharpeand Bradley(RSB) to characterize the instability of detonations. While it is well established that the ignition delay provides a good measure for detonability, the RSB acceleration, or its non-dimensionalform , provides a further discriminant between mixtures with similar ignition delays. The present assessment of detonability reveals that while a stoichiometric mixture of hydrogen-air has an ignition delay one and two orders of magnitude shorter than, respectively, propane and methane, hydrogen also has a parameter smaller by respectively one and two orders of magnitude. Its smaller propensity for instability is reflected by an RSB acceleration parameter similar to the two hydrocarbons. The predictions however indicate that lean hydrogen mixtures are likely to be much more unstable than stoichiometric ones. The relation between the parameter and potential to amplify an unstable transverse wave structure has been further determined through numerical simulation of decaying reactive Taylor-Sedov blast waves. Using a simplified two-step model calibrated for these fuels, we show that methane mixturesdevelop cellular structuresmore readily than propane andhydrogen, when observed on similar induction time scales.Future work should be devoted towards a quantitative inclusion of the RSB parameter in assessing the detonability of a given mixture.