The case-crossover design provides a means to study the effects of transient exposures on the risk of acute illness, for example, the effects of drinking alcohol on the immediate risk of a heart attack. Only cases are required by the design, since each case is effectively its own control; what a case was doing at the time of an acute event is compared with what the case would have been doing usually. Maclure has described an approach based on the Mantel-Haenszel method of analysis. It is shown here how the analysis of case-crossover designs can be achieved by a method of maximum likelihood. The method is quite general and, in principle, can be used to analyse the joint effects of many transient exposures. For binary exposures the Mantel-Haenszel approach is an approximate solution to the likelihood equations. In practice, case-crossover designs are limited by the information available on each case's 'usual' behaviour. Extracting such information requires in-depth questioning, but, in principle, it can be obtained. To do so requires careful questionnaire design. The approach is illustrated by analysis of 24 hour alcohol consumption and the risk of myocardial infarction. The problem with this analysis is how to estimate the probability of what a case would 'usually' have been doing from information on drinking frequency.