Properties, which have long been used for reasoning about systems, are sets of traces. Hyperproperties, introduced here, are sets of properties. Hyperproperties can express security policies, such as secure information flow, that properties cannot. Safety and liveness are generalized to hyperproperties, and every hyperproperty is shown to be the intersection of a safety hyperproperty and a liveness hyperproperty. A verification technique for safety hyperproperties is given and is shown to generalize prior techniques for verifying secure information flow. Refinement is shown to be valid for safety hyperproperties. A topological characterization of hyperproperties is given.