The structure, flame speed and stability of freely propagating combustion waves in rich hydrogen-air mixtures is investigated numerically using models with detailed and reduced two-step kinetic mechanisms. The critical conditions for the onset of diffusive-thermal pulsating instabilities are found in the equivalence ratio vs pressure parameter plane in each case. The oscillating solutions emerging as a result of these instabilities are investigated. It is demonstrated that the models with reduced kinetics are able to qualitatively (models with constant density) and quantitatively (models with variable density) predict the flame characteristics and stability as compared to the models with detailed reaction mechanism. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.