Recent research shows that adults’ neural oscillations track the rhythm of the speech signal. However, the extent to which this tracking is driven by the acoustics of the signal, or by language-specific processing remains unknown. Here adult native listeners of three rhythmically different languages (English, French, Japanese) were compared on their cortical tracking of speech envelopes synthesized in their three native languages, which allowed for coding at each of the three language’s dominant rhythmic unit, respectively the foot (2.5 Hz), syllable (5 Hz), or mora (10 Hz) level. The three language groups were also tested with a sequence in a non-native language, Polish, and a non-speech vocoded equivalent, to investigate possible differential speech/nonspeech processing. The results first showed that cortical tracking was most prominent at 5 Hz (syllable rate) for all three groups, but the French listeners showed enhanced tracking at 5 Hz compared to the English and the Japanese groups. Second, across groups, there were no differences in responses for speech versus non-speech at 5 Hz (syllable rate), but there was better tracking for speech than for non-speech at 10 Hz ( not the syllable rate). Together these results provide evidence for both language-general and language-specific influences on cortical tracking.