Three stages of modelling the monthly number of accidents and deaths are possible, ranked in order of increasing complexity according to the Box-Jenkins methodology: (i) the univariate model; (ii) the univariate model with dummy variable; (iii) the multivariate model. By means of the transformation of the number of accidents by logarithmic function, these additive types of model become multiplicative with elasticity; the latter is much easier to handle at the interpretation stage. The greatly improved analytical capacity that more complex models allow is illustrated by means of an analysis of the evolution of the monthly number of deaths in France during the period from 1970 to 1977. The stochastic components of the time series are estimated by the univariate model, the effects of the speed-limiting and belt-wearing countermeasures by the univariate model with dummy variable and the influence of speeds and beltwearing taking account of traffic volume by the multivariate model. These models have made it possible (i) to estimate the safety gain achieved by more widespread belt-wearing and that achieved by a narrowing of the range of speeds practised, and (ii) to conclude that there is only a small influence upon safety brought about by changes in the average speeds of private cars and other vehicles of similar mass.