We used an age-period-cohort model with arbitrary constraints on the parameters, fitted to the mortality data for the period 1955-84, to project rates in mortality from all cancers and 11 major cancer sites in Italy for the period 1985-1999. For all neoplasms considered, using estimated age and cohort values, two models were fitted, one based on constant period effects, and one on a linear regression on the logarithm of the six calendar periods. Furthermore, "a priori" defined coefficients based on epidemiologic inferences were given to period values for tobacco-related neoplasms (below unity for males, above unity for females, on the basis of recent trends in tobacco prevalence in the two sexes), for breast and ovarian cancer (in relation to the potentially different effect of oral contraceptives, other female hormones, reproductive factors and treatment on these neoplasms), and for total cancer mortality. This produced a range of potential estimates, which were reasonably similar for neoplasms (such as stomach, intestines, breast, ovary or prostate) for which no major change in slope of the cohort effects was evident, but wider (i.e., between 188 and 264/100,000 males aged 40 to 79 in 1995-99) for lung or other tobacco-related cancers. Although this range of variation is far from negligible, the estimated values indicate that lung cancer among Italian males aged 40 to 79, even under the more optimistic assumption, will probably be higher at the end of the century than in the early 1980's, and that lung cancer alone will account for 35 to 42% of all cancer deaths in males between 40 and 79 years. Though any prediction has, by definition, inherent difficulties and uncertainties, cancer mortality in the near future will be strongly influenced by age and cohort effects already known, and hence its projections may offer some indication of public health relevance.