Surveillance is an important class of applications for wireless senor networks (WSNs), whose central task is to detect events of interest. Existing approaches seriously suffer from blind spots and low energy efficiency. In this paper, we propose a fully distributed algorithm GAP for energy-efficient event detection for surveillance applications. The unique features of GAP are threefold. First, it provides guaranteed detectability for any event occurring in the sensing field. Second, it exposes a convenient interface of the user to specify the desired detectability. Finally, it significantly reduces the duty cycle of each sensor and therefore prolongs system lifetime remarkably. Without relying on costly time synchronization, GAP is a lightweight distributed protocol and is truly scalable to network scale and sensor density. Comprehensive experiments are conducted, which demonstrate the efficacy of the GAP algorithm.