This paper presents a formalization in the duration calculus (DC) of scheduling policies for tasks with shared resources. Two frameworks are presented for specifying classes of schedulers. With these specifications, some properties of these schedulers were proved using the formal deduction of DC. This paper aims to encourage other researchers to formally treat real-time aspects of operating systems which in the past were conventionally a piece of ad hoc territory in computer science. Philip Chan is a Fellow of UNU/IIST, on leave from the Department of Software Technology, College of Computer Studies, De La Salle University, Manila, Philippines, where he is an assistant professor. His current research interests include operating systems, distributed operating systems, and Duration Calculus. His e-mail address at UNU/IIST is pc@iist.unu.edu and at De La Salle University is ccspc@linux1.dlsu.edu.ph Dang Van Hung is from the Institute of Information Technology of National Center for Natu...