Quadratic time-frequency representations (TFRs) and time-scale representations (TSRs) have been shown to be very useful for detecting nonstationary signals in the presence of nonstationary noise. The theory developed thus far is only for the single observation case; however, in many situations involving signal detection, there are advantages in using an array of receiving sensors. Sensor arrays allow for target or source localization and can provide a large gain in the SNR. We show that time-frequency and time-scale representations provide a natural structure for the detection of a large class of nonstationary signals in the presence of nonstationary noise using an array of sensors. That is, time-frequency and time-scale provide a detection structure that is both optimal and allows for efficient implementation. In developing the TFR/TSR-based optimal quadratic array processor, we consider several types of array environments including those with full, partial, and no coherence.