A class of decentralized sequential detection problems is considered for which multiple sensors are used and a global decision is desired. Two hypotheses and two detectors are considered. The detectors do not communicate but their decisions are coupled through a fusion rule. It is shown that at each time instant, the local decision rules are characterized by likelihood-ratio tests (LRT) and thresholds. However, the thresholds are coupled at all times. Because of this coupling, the thresholds are determined by solving all of the equations simultaneously.