When the ignition of a car engine is switched off, the engine normally comes to rest within a few revolutions but, occasionally, it may continue to fire erratically for a few seconds or longer. This phenomenon is known as run-on and, for the majority of European engines, is the result of spontaneous ignition of the fuel-air mixture in the combustion chamber. Part 1 of this paper describes experiments in a single-cylinder research engine which have been made to establish the principles controlling run-on. In particular the effects of air/fuel ratio, the nature of the fuel and the pressure-temperature-time history of the fuel-air mixture in the combustion chamber have been studied, as it is known that these factors play an important part in spontaneous ignition in experiments in laboratory vessels. From these observations it has been possible to formulate a theoretical model of the run-on process which explains the salient features of the phenomenon. In particular, it shows how the gradual cooling of the engine limits the duration of run-on and also how the duration of run-on may be considered as a measure of the extent to which fuel or engine factors must be altered to eliminate run-on. Part 2 describes the application of these principles to car engines using normal commercial-type fuels. It is concluded that the following are important features in the control of run-on: the use of fuel of sufficiently high Research octane number, minimum opening of throttle at idle, sufficient time for cooling of the combustion chamber before the ignition is switched off, efficient engine cooling, and small valve overlap. Current devices for reducing exhaust emissions are likely, through their effects on these features, to increase the tendency of an engine run-on. Combustion chamber deposits, though, appear to have little influence.