The human auditory system has evolved to efficiently process individual streams of speech. However, obtaining temporally detailed responses to distinct continuous natural speech streams has hitherto been impracticable using standard neurophysiological techniques. Here a method is described which provides for the estimation of a temporally precise electrophysiological response to uninterrupted natural speech. We have termed this response AESPA (Auditory Evoked Spread Spectrum Analysis) and it represents an estimate of the impulse response of the auditory system. It is obtained by assuming that the recorded electrophysiological function represents a convolution of the amplitude envelope of a continuous speech stream with the to-be-estimated impulse response. We present examples of these responses using both scalp and intracranially recorded human EEG, which were obtained while subjects listened to a binaurally presented recording of a male speaker reading naturally from a classic work of fiction. This method expands the arsenal of stimulation types that can now be effectively used to derive auditory evoked responses and allows for the use of considerably more ecologically valid stimulation parameters. Some implications for future research efforts are presented.