Commercial fuels are mixtures with large numbers of components. Continuous thermodynamics is a technique for modelling fuel mixtures using a probability density function rather than dealing with each discreet component. The mean and standard deviation of the distribution are then used to model the chemical reactions of the mixture. This thesis develops the necessary theory to apply the technique of continuous thermodynamics to the oxidation reactions of hydrocarbon fuels. The theory is applied to three simplified models of hydrocarbon oxidation: a global one-step reaction, a two-step reaction with CO as the intermediate product, and the four-step reaction of Müller et al. (1992), which contains a high- and a low-temperature branch. These are all greatly simplified models of the complex reaction kinetics of hydrocarbons, and in this thesis they are applied specifically to n-paraffin hydrocarbons in the range from n-heptane to n-hexadecane. The model is tested numerically using a simple constant pressure homogeneous ignition problem using Cantera and compared to simplified and detailed mechanisms for n-heptane. The continuous thermodynamics models are able not only to predict ignition delay times and the development of temperature and species concentrations with time, but also changes in the mixture composition as reaction proceeds as represented by the mean and standard deviation of the distribution function. Continuous thermodynamics is therefore shown to be a useful tool for reactions of multicomponent mixtures, and an alternative to the "surrogate fuel" approach often used at present.