Abstract: Program observation deals with the behavior properties in one execution of a program.For Lack of global information,observing a distributed program is intrinsically difficult.The core of distributed program observations is a global property detection problem.A methodological sort of global property detection is proposed.General methods for global property detection,i.e.,snapshot methods for stable properties,global state lattice based methods for unstable properties,and language recognition methods for dynamic properties,are discussed.Special methods for specific global properties,such as strongly/locally stable properties,conjunctive predicates,and flow/wave pattern dynamic properties,are also presented.