The problem of distributed detection involving N sensors is considered. The configuration of sensors is serial in the sense that the (j-1)th sensor passes its decision to the jth sensor and that the jth sensor decides using the decision it receives and its own observation. When each sensor employs the Neyman-Pearson test, the probability of detection is maximized for a given probability of false alarm, at the Nth stage. With two sensors the serial scheme is better than the parallel fusion scheme analyzed in the literature. For certain distributions of observations, the serial scheme performs better for all N. Numerical examples illustrate the global optimization by the selection of operating thresholds at the sensors.