The task of determining patients' eligibility for clinical trials is knowledge and data intensive. In this paper, we present a model for the task of eligibility determination, and describe how a computer system can assist clinical researchers in performing that task. Qualitative and probabilistic approaches to computing and summarizing the eligibility status of potentially eligible patients are described. The two approaches are compared, and a synthesis that draws on the strengths of each approach is proposed. The result of applying these techniques to a database of HIV-positive patient cases suggests that computer programs such as the one described can increase the accrual rate of eligible patients into clinical trials. These methods may also be applied to the task of determining from electronic patient records whether practice guidelines apply in particular clinical situations.