A detailed chemical kinetic reaction mechanism is developed for the five major components of soy biodiesel and rapeseed biodiesel fuels. These components, methyl stearate, methyl oleate, methyl linoleate, methyl linolenate, and methyl palmitate, are large methyl ester molecules, some with carbon-carbon double bonds, and kinetic mechanisms for them as a family of fuels have not previously been available. Of particular importance in these mechanisms are models for alkylperoxy radical isomerization reactions in which a C=C double bond is embedded in the transition state ring. The resulting kinetic model is validated through comparisons between predicted results and a relatively small experimental literature. The model is also used in simulations of biodiesel oxidation in jet-stirred reactor and intermediate shock tube ignition and oxidation conditions to demonstrate the capabilities and limitations of these mechanisms. Differences in combustion properties between the two biodiesel fuels, derived from soy and rapeseed oils, are traced to the differences in the relative amounts of the same five methyl ester components.