There is controversy about cancer mortality trends; some analyses show increasing mortality, but others suggest that rates are falling in the youngest age groups. We have investigated trends in cancer incidence in the whole of Sweden for the period 1958 to 1987. 837,085 cancer cases were registered during the period studied. Incidence rate patterns were studied by age-period-cohort modelling. The risk of cancer was higher for people born during the 1950s than for those born in 1873-82; for women the risk was doubled and for men it was trebled. Although the rate of increase slowed, it showed no sign of levelling off in the youngest birth cohorts. The frequency of smoking-related cancers increased greatly in both sexes, but such tumours could explain only part of the rise in total cancer. These trends predict a continuing rise in the incidence rate of cancer, and suggest a worrying pattern of increasing population exposure to carcinogenic influences.