By properly weighting and summing the individual signals received by an array of acoustic sensors, the performance of the array can be improved. In order that the weights can be chosen in a rational manner, some mathematical model must be postulated for the received array data. In this study we examine the effects of a class of data modeling errors on the directivity of linear and nonlinear array processors. We derive a measure of the extent to which the array response may change as a result of Gaussian deviations of the amplitude and phase of the modeled data from those of a nominal model. Among all array processors the simple beamformer is shown to have minimum sensitivity to small model perturbations of this type, and thus to be robust to errors in model selection. For a certain proposed high-resolution estimator, we show that cases exist in which the sensitivity is very large. An array processor having large sensitivity to modeling errors is mathematically analogous to a superdirective electromagnetic array, with the data model perturbations corresponding to perturbations in the exciting currents, or radiator positions, of the latter. Large perturbation sensitivity of an accoustic array processor is analogous to superdirectivity in phased array antenna design.