In most scenarios where detonations in fuel-air mixtures can present a hazard, such as in industrial accidents, or where they can be used for practical purposes, like detonative propulsion applications, the mixture is essentially non-uniform. For industrial accidents, it is important to understand what fraction of the mixture can detonate in order to limit the consequences of an explosion event by ensuring proper separation distances to critical facilities and personnel. For propulsion applications, mixture non-uniformities directly affect the performance of the device by limiting the detonable portion of the mixture. While it is known that detonation limits depend on mixture composition, geometry, and concentration gradients, these limits have only been defined for either uniform mixtures, or for detonation propagation in the direction of a smooth concentration gradient. In this study, a model is developed to generalize these classic detonation limits to consider arbitrary concentration distributions and is compared with experimental data for detonation propagation in non-uniform mixtures. The model is then applied to representative concentration distributions corresponding to two practical examples, a high-pressure hydrogen jet and a large-scale vapor cloud explosion (VCE). For both distributions, the model illustrates how a non-uniform mixture composition significantly limits the detonable portion of the flammable mixture created by a realistic release. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.