Trust management is a form of distributed access control that allows one principal to delegate some access decisions to other principals using distributed policy statements. While this makes trust management more flexible than the access matrix model, it makes safety and security analysis more important. In this work, we study security properties such as safety and availability for a family of trust management languages, devising algorithms for deciding the possible consequences of certain changes in policy. We show that in contrast to the undecidability of classical Harrison-Ruzzo-Ullman result, our primary security properties are decidable. In particular, most safety properties we study are decidable in polynomial time. The computational complexity of containment analysis, the most complicated security property we study, forms a complexity hierarchy based on the expressive power of the trust management language. This is joint work with Prof. John Mitchell of Stanford University and Dr. William Winsborough of George Mason University.