Any screening program based on a quantitative risk factor has the objective of identifying individuals at high risk of disease. When the risk factor varies within individuals over time or is subject to measurement error, repeat measurements should aid risk assessment. This article presents statistical guidelines for sequential screening based on measurements accumulated over time. The aim for each subject is to decide whether (a) risk is sufficiently low that screening can be stopped, or (b) risk is sufficiently high that intervention is indicated, or (c) further measurements should be obtained to improve risk assessment. The guidelines presented are optimal in a population, public health sense; that is, they are designed to give the maximal expected risk in the group identified for intervention, subject to constraints on that group's size and on the cost of screening (defined in terms of the average number of measurements per person required). An example concerning screening for cardiovascular disease in middle-aged men using diastolic blood pressure measurements is presented.