This paper studies two classes of hazard-rate-based models for the mortality in a group of individuals taking normal life expectancy into account. In a multiplicative hazard model, the estimate for the relative mortality generalises the standardised mortality ratio, and the adequacy of a model with constant relative mortality can be tested using a type of total time on test statistic. In an additive hazard model, continuous-time generalisations of a "corrected" survival curve and a "normal" survival curve are obtained, and the adequacy of a model with constant excess mortality can again be tested using a type of total time on test statistic. A model including both the multiplicative hazard model and the additive hazard model is briefly considered. The use of the models is illustrated on a set of data concerning survival after operation for malignant melanoma.