Abstract Periodic screening programs for the early detection of chronic diseases such as cancer and heart disease may not always lead to a reduction in the number of deaths from the disease. Some improvement is usually possible with the use of a more sensitive detection test, or by lowering the age for the first screening examination, or by decreasing the period between examinations. However, the extent of the reduction in deaths that is attainable with these changes is limited by the underlying biological behavior of the disease as well as by the rate at which the disease is detected without the screening examination, i.e., by the “natural history” of the disease. The effectiveness of a periodic screening program is derived as a function of this natural history, the period between examinations, the sensitivity of the detection test, the age at the first examination, and the age distribution of the rate of the disease initiation in the screened population. A detailed discussion is given of how these results might be used to estimate the effectiveness of any planned periodic screening program. The analysis of a simple example suggests that for some diseases decreasing the interval between screening examinations may not lead to a significant lowering of the death rate, i.e., there may be a natural lower bound on the screening period.