Whether syntactic and semantic processes during sentence comprehension follow strict sets of rules or succumb to context-dependent heuristics was studied by recording event-related potentials in a dual-task design. In one condition, sentence-extraneous acoustic material was either semantically congruent or incongruent relative to an adjective in the visually presented sentence, the latter being either semantically correct or incorrect within the sentence context. Homologous syntactic (gender) manipulations were performed in another condition. Syntactic processing within the sentence appeared to be blind to the syntactic content of the second task. In contrast, semantically incongruous material of the second task induced fluctuations typically associated with the detection of within-sentence semantic anomalies (N400) even in semantically correct sentences. Subtle but extant differences in topography between this N400 and that obtained with within-sentence semantic violations add to recent proposals of separate semantic subsystems differing in their specificity for sentence structure and computational procedures. Semantically incongruous material of the second task also influenced later stages of the processing of semantically incorrect adjectives (P600 component), which are traditionally assumed to pertain to the syntactic domain. This result is discussed in the light of current proposals of a third combinatorial stream in sentence comprehension.