We describe a layered approach to access control for distributed and interoperable computing systems. Firstly, compound access control policies are conceptually specified, using the policy algebra proposed by Bonatti/Capitani di Vimercati/Samarati. Secondly, SPKI/SDSI is exploited to implement and to enforce a policy specification by means of credentials. Therefore, SPKI/SDSI is slightly extended, in particular in order to deal with the subtraction operator of the algebra and to allow algebraic expressions over local names as subjects in authorization certificates. Besides presenting the overall approach, the paper elaborates some details for a still powerful fraction of the policy algebra, thereby examining the correctness of the credential-based implementation.