Role-Based Access Control (RBAC) is a widely used model for expressing access control policies. In large organizations, the RBAC policy may be collectively managed by many administrators. Administrative RBAC (ARBAC) models express the authority of administrators, thereby specifying how an organization's RBAC policy may change. Changes by one administrator may interact in unintended ways with changes by other administrators. Consequently, the effect of an ARBAC policy is hard to understand by simple inspection. In this paper, we consider the problem of analyzing ARBAC policies. Specifically, we consider reachability properties (e.g., whether a user can eventually be assigned to a role by a group of administrators), availability properties (e.g., whether a user cannot be removed from a role by a group of administrators), containment properties (e.g., every member of one role is also a member of another role) satisfied by a policy, and information flow properties. We show that reachability analysis for ARBAC is PSPACE-complete. We also give algorithms and complexity results for reachability and related analysis problems for several categories of ARBAC policies, defined by simple restrictions on the policy language. Some of these results are based on the connection we establish between security policy analysis and planning problems in Artificial Intelligence.