Emerging evidence from neuroimaging and neuropsychology suggests that human speech comprehension engages two types of neurocognitive processes: a distributed bilateral system underpinning general perceptual and cognitive processing, viewed as neurobiologically primary, and a more specialized left hemisphere system supporting key grammatical language functions, likely to be specific to humans. To test these hypotheses directly we covaried increases in the nonlinguistic complexity of spoken words [presence or absence of an embedded stem, e.g., claim (clay)] with variations in their linguistic complexity (presence of inflectional affixes, e.g., play+ed). Nonlinguistic complexity, generated by the on-line competition between the full word and its onset-embedded stem, was found to activate both right and left fronto-temporal brain regions, including bilateral BA45 and -47. Linguistic complexity activated left-lateralized inferior frontal areas only, primarily in BA45. This contrast reflects a differentiation between the functional roles of a bilateral system, which supports the basic mapping from sound to lexical meaning, and a language-specific left-lateralized system that supports core decompositional and combinatorial processes invoked by linguistically complex inputs. These differences can be related to the neurobiological foundations of human language and underline the importance of bihemispheric systems in supporting the dynamic processing and interpretation of spoken inputs.