Parameters characterising the progression of cervical neoplasia were estimated from population-based cancer and mortality statistics in Sweden for 1958-1981 by means of a dynamic computer model. Proceeding from that model and these data, the incidence and prevalence curves were constructed, the effects of the extensive cytological screening measures introduced during the 1960s were assessed, and future gains due to the measures already undertaken up to 1981 could be simulated. About 4,000 cases of cancer in situ were diagnosed annually in Sweden after the end of the 1960s, most of them in women born later than 1919. The maximum reduction in the number of invasive cancers up to 1981 was 42% for women born in 1919-1923, but increased progressively for later birth cohorts and reached 69% for those born in 1934-1938. The corresponding reduction in mortality rates was of the same magnitude. The screening measures up to 1981 will ultimately result in a reduction of invasive cancer by about 12,500 cases and of the number of deaths due to this disease by about 4,100. Only a part of the total gain in the number of lives saved had been revealed at the end of the study period in 1981.