Studies of perception have long shown that the brain adds information to its sensory analysis of the physical environment. A touchstone example for humans is language use: to comprehend a physical signal like speech, the brain must add linguistic knowledge, including syntax. Yet, syntactic rules and representations are atemporal (i.e., abstract and not bound by time), so they must be translated into time-varying signals for speech comprehension and production. Here, we test three different models of the temporal spell-out of syntactic structure against brain activity of people listening to Dutch stories: an integratory bottom-up parser, a predictive top-down parser, and a mildly predictive left-corner parser. These models build exactly the same structure but differ in when syntactic information is added by the brain - this difference is captured in the (temporal distribution of the) complexity metric 'incremental node count'. Using temporal response function models with both acoustic and information-theoretic control predictors, node counts were regressed against source-reconstructed delta-band activity acquired with magnetoencephalography. Neural dynamics in left frontal and temporal regions most strongly reflect node counts derived by the top-down method, which postulates syntax early in time, suggesting that predictive structure building is an important component of Dutch sentence comprehension. The absence of strong effects of the left-corner model further suggests that its mildly predictive strategy does not represent Dutch language comprehension well, in contrast to what has been found for English. Understanding when the brain projects its knowledge of syntax onto speech, and whether this is done in language-specific ways, will inform and constrain the development of mechanistic models of syntactic-structure building in the brain.