The method described by Bryn [J. Acoust. Soc. Amer.34, 289–297 (1962)] and Vanderkulk [J. Brit. IRE26, 285–292 (1965)] for analyzing optimum passive detection of weak stationary Gaussian plane waves in additive stationary Gaussian noise is applied to a linear array of hydrophones which may be closely spaced. The advantage in optimum over conventional delay‐sum‐square‐integrate processing is assessed in various situations. At a particular temporal frequency, the noise is characterized by a spatially derived spectrum. If this noise spectrum is reasonably flat over the principal response band of the steered array and if there are no effects from outside this band, then conventional processing will produce almost as high an array gain as the optimum detector. This situation is expected in reasonably isotropic noise fields at steerings near broadside. For long arrays of closely spaced hydrophones, a quantity termed theBLproduct roughly expresses the flatness of the spatial noise spectrum in the response band. When theBLproduct is high, the maximum nonsuperdirective array gain is simply the inverse of the spatial spectrum properly scaled. This gain is achieved by conventional processing the absence of strong interference; otherwise it is achieved by a weighting of the spatial spectrum, e.g., by a partial nulling.