In this paper we define formally a wide variety of separation-of-duty (SoD) properties, which include the best known to date, and establish their relationships within a formal model of role-based access control (RBAC). The formalism helps remove all ambiguities of informal definition, and offers a,wide choice of implementation strategies. We also explore the composability of SoD properties and policies under a simple criterion. We conclude that practical implementation for SoD policies requires new method's and tools for security administration even within applications that already, support RBAC, such as most database management systems.