A complex signal composed of a fundamental (525 cps) and a second harmonic (1050 cps) was created by systematically altering the phase of the second with respect to the first through six relative‐phase relationships (0°, 30°, 60°, 90°, 120°, and 150°). Four 100‐msec bursts of noise, one of which contained the complex waveform, were presented to four subjects; and they were forced to choose which of the four contained the signal. Ten different signal‐to‐noise ratios (S/N), covering a range of 10 dB around a subjective “threshold” value, were utilized. Forty judgments at each of these S/N ratios were made in each phase condition. The data revealed differences with regard to the detectability of the complex signal as a function of the relative phase of the components.