The observed mortality of a group of individuals often needs to be compared with that expected from the death rates of the national population, with allowance made for age and period. Expected deaths are usually calculated by the subject-years method (Case and Lea, 1955, British Journal of Preventive and Social Medicine 9, 62-72), in which each person is assumed at risk up to the date of the analysis, the date of death, or the date the person was lost to follow-up, whichever is first. Some of the properties of this method are described, including an approach based on likelihood. For this purpose the observed number of deaths may be treated as though it were a Poisson variable. The likelihood approach leads to a generalization to the cases where the groups have a factorial structure or where covariates are available for each individual. The calculations are readily carried out by use of GLIM or GENSTAT.