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Can neural rhythms reflect purely internal syntactic processes in multi-word constructions? To test this controversial conjecture - relevant to language in particular and cognition more broadly - we recorded electroencephalographic and behavioural data as participants listened to isochronously presented sentences of varying in syntactic complexity. Each trial comprised ten concatenated sentences and was either fully grammatical (regular) or rendered ungrammatical via randomly distributed word order violations. We found that attending the regular repetition of abstract syntactic categories (phrases and sentences) generates neural rhythms whose harmonics are mathematically independent of word rate. This permits to clearly separate endogenous syntactic rhythms from exogenous speech rhythms. We demonstrate that endogenous but not exogenous rhythms predict participants’ grammaticality judgements, and allow for the neural decoding of regular vs. irregular trials. Neural harmonic series constitute a new form of behaviourally relevant evidence for syntactic competence.