Traditional electrophysiological methods to study temporal auditory processing of the fundamental frequency of the voice (f0) often use unnaturally repetitive stimuli. In this study, we investigate f0 processing of meaningful continuous speech. EEG responses evoked by stories in quiet were analysed with a novel ’f0-tracking’ method that uses linear models to characterize both the strength and the spatiotemporal properties of the f0 response. Different samples of continuous speech (six stories by four speakers: two male and two female) were used to investigate stimulus effects on the f0 response. The results indicated stronger f0-tracking for the male-narrated stories compared to the female-narrated stories, for which many responses were not significant. Moreover, response strength was inversely related to the f0 of the speaker and the rate of f0 change throughout the story. These effects likely occur because phase-locking to the f0 is more challenging when the f0 is higher and/or more variable. From additional experiments, we conclude that female-narrated stories can be successfully used for continuous f0 responses but only if the rate of f0-change is low and the harmonic content is strong. Most natural female voices do not have these characteristics, so careful stimulus selection is required. The spatio-temporal analysis revealed a centrally-located peak response with latency between 7 and 12 ms for the female-narrated stories, suggestive of a brainstem source. In contrast, for male-narrated stories the analysis indicated at least two sources: one source with a latency of 13-15 ms, likely in the brainstem, and one right-dominant posterior temporal source with a latency of 23-25 ms, suggestive of the right primary auditory cortex. This adds to the growing evidence that auditory responses to frequencies in the lower range of the f0 (e.g. most male voices) do not originate solely from the brainstem but have additional cortical contributions. In conclusion, the novel f0-tracking method was successfully applied to a range of continuous speech samples and the findings on temporal processing of the f0 are in line with earlier findings from repetitive stimulus paradigms. The novel method is recommended over traditional paradigms because continuous speech is more relevant for day-to-day conversation and more engaging for the subjects, but also because the method allows for extensive analysis of both response strength and spatio-temporal characteristics.