In an experiment involving 950 mice with a normal lifespan of 2-3 years, in laboratory conditions, regular benzpyrene application to the skin was started at 10, 25, 40 or 55 weeks of age. The incidence rate of malignant epithelial tumours among the survivors in each group increased steeply with time. This increase was associated directly with duration of exposure but, given duration, was independent of age at the start of exposure, as were the growth rates of already established tumours. In our experiment, although age per se was irrelevant, the cancer incidence rate increased approximately as a power of the duration of exposure to benzpyrene. This shows that the observed approximate power-law increase of most human adult cancer incidence rates with age could exist merely because age equals duration of exposure to background and spontaneous carcinogenic stimuli. Thus, no intrinsic effects of ageing (such as failing immunological surveillance or age related hormonal changes) whatever need to postulated to explain the vast increases in old age of the incidence rates of such human cancers. This result can greatly simplify speculation about mechanisms of carcinogenesis.