In longitudinal studies data is collected in a series of waves. Each wave after the first suffers from attrition. Therefore it can be difficult to discriminate between changes in sample parameters due to a longitudinal process (e.g. ageing) and changes due to attrition. The problem is particularly vexing if one of the purposes is to compare differences between two or more groups over time, because there may be differential attrition across groups. We refer to this as a "recruitment" problem, because the sample studied in any wave after the first can be thought of as having been recruited from a preceding wave. We present a mathematical model of the recruitment process. We then apply it to two large longitudinal studies, the British Cohort Survey 1970 and the National Child Development Study (1958), to demonstrate how we can identify effects expected from recruitment alone. As an illustration we show that differential recruitment would predict increasing differences between estimates of men's and women's intelligence as the studied sample ages. (Contains 6 tables and 2 figures.)