A transient one-dimensional reactive-diffusive model is used to simulate the process of post-flame oxidation of unburned hydrocarbons in spark-ignition engines, and to identify the physical and chemical factors controlling the oxidation process. The model focuses on the oxidation processes laking place in the reactive layer between hot burned gases and cold unreacted air/fuel mixture, with initial and boundary conditions similar to those provided by the emergence of hydrocarbons from a piston land crevice. Energy and species conservation equations are solved for the entire time-dependent process, using detailed chemical kinetic mechanisms. Simulation results show that the in-cylinder process is largely controlled by diffusion rates for burned gas temperatures above a transition level (of the order of 1400 - 1700 K depending on fuel type), reaction controlled for temperatures below that level, and practically frozen for temperatures below 1300 K. Radicals in the burned gas are shown to be important only in initiating the reaction, as radicals concentrations generated by the oxidating fuel greatly exceed burned gas concentrations except at burned gas temperatures below 1300 K. Large differences in oxidation rates are found for different fuels for the same initial conditions of burned gas temperatures and stoichiometries. The differences can be attributed to the lengths of the reaction chain, and the diffusion of intermediate products towards the cold wall zone (which acts as a storage buffer), leading to differences in the generation of radicals in the reacting zone. In contrast with previous suggestions that oxidation is dominated by the existing radicals in the burned gas, the simulations show that the role of chemical kinetics and the self-generation of radicals are critical in determining overall oxidation rates. Further, the simulations suggest that measured hydrocarbon emission levels from operation on different fuels may be attributed to their drastically different oxidation pathways and rates, rather than simply volatility or solubility in lubricant oil.