The many studies of cancer made in recent years have revealed that the preclinical period of cancer--the period from carcinogenic transformation of a cell to growth of an overt tumor when the diagnosis of "cancer" is made--is longer and has a larger variance than considered formerly. Based on these results, the existing multistage theory of carcinogenesis has been reviewed and modified in this paper. In the newly obtained model, which is designated "initiation-manifestation model," it is assumed that carcinogenesis is a combination of two different processes, i.e., carcinogenic transformation of one cell and the subsequent manifestation of cancer. Further, we assumed that the lengths of these two periods are stochastic variables having gamma distributions, and that they are mutually independent. Applying this model, the actual morbidity of various types of human adult cancer was analyzed.