A new method of using chemical kinetic reaction modeling to predict the Research Octane Number (RON) and Motor Octane Number (MON) of single component fuels and fuel mixtures is described and illustrated via comparisons between computed and experimental values obtained using the well-established ASTM test procedures in a Cooperative Fuels Research (CFR) engine. Comparisons include predictions of RON and MON for a large variety of neat fuels, studies determining the RON and MON of mixtures of primary reference fuels (PRF) and toluene, and studies of RON and MON for mixtures of single-component and multiple-component gasoline surrogate mixtures with ethanol. Advantages in costs, time, and experimental complexity of the kinetic modeling approach compared to the existing engine test procedures are discussed. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.