Privacy is considered critical for all organizations needing to manage individual related information. As such, there is an increasing need for access control models which can adequately support the specification and enforcement of privacy policies. In this paper, we propose a model, referred to as Conditional Privacy-aware Role Based Access Control (P-RBAC), which supports expressive condition languages and flexible relations among permission assignments for more complex privacy policies. Efficient algorithms for detecting conflicts, redundancies, and indeterminism for a set of permission assignments are presented. In the paper we also extend Conditional P-RBAC to Universal P-RBAC by taking into account hierarchical relations among roles, data and purposes. In comparison with other approaches, such as P3P, EPAL, and XACML, our work has achieved both expressiveness and efficiency.