With the rapid proliferation of software agents, there comes an increased need for agents to ensure that they do not provide data and/or services to unauthorized users. We first develop an abstract definition of what it means for an agent to preserve data/action security. Most often, this requires an agent to have knowledge that is impossible to acquire --- hence, we then develop approximate security checks that take into account, the fact that an agent usually has incomplete/approximate beliefs about other agents. We develop two types of security checks --- static ones that can be checked prior to deploying the agent, and dynamic ones that are executed at run time. We prove that a number of these problems are undecidable, but under certain conditions, they are decidable and (our definition of) security can be guaranteed. Finally, we propose a language within which the developer of an agent can specify her security needs, and present provably correct algorithms for static/dynamic security verification. (Also cross-refernced as UMIACS-TR-99-62)