We introduce a general framework for reasoning about secrecy and privacy requirements in multiagent systems. Our definitions extend earlier definitions of secrecy and nondeducibility given by Shannon and Sutherland. Roughly speaking, one agent maintains secrecy with respect to another if the second agent cannot rule out any possibilities for the behavior or state of the first agent. We show that the framework can handle probability and nondeterminism in a clean way, is useful for reasoning about asynchronous systems as well as synchronous systems, and suggests generalizations of secrecy that may be useful for dealing with issues such as resource-bounded reasoning. We also show that a number of well-known attempts to characterize the absence of information flow are special cases of our definitions of secrecy.