The study investigated the processing of sound motion, employing a psychophysical motion discrimination task in combination with electroencephalography. Following stationary auditory stimulation from a central space position, the onset of left- and rightward motion elicited a specific cortical response that was lateralized to the hemisphere contralateral to the direction of motion. The contralaterality of the motion onset response decreased when the velocity was reduced. Higher motion velocity was associated with larger and earlier cortical responses and with shorter reaction times to motion onset. The results indicate a close correspondence of brain activity and behavioral performance in auditory motion detection.