Language processing engages large-scale functional networks in both hemispheres. Although it is widely accepted that left perisylvian regions have a key role in supporting complex grammatical computations, patient data suggest that some aspects of grammatical processing could be supported bilaterally. We investigated the distribution and the nature of grammatical computations across language processing networks by comparing two types of combinatorial grammatical sequences—inflectionally complex words and minimal phrases—and contrasting them with grammatically simple words. Novel multivariate analyses revealed that they engage a coalition of separable subsystems: inflected forms triggered left-lateralized activation, dissociable into dorsal processes supporting morphophonological parsing and ventral, lexically driven morphosyntactic processes. In contrast, simple phrases activated a consistently bilateral pattern of temporal regions, overlapping with inflectional activations in L middle temporal gyrus. These data confirm the role of the left-lateralized frontotemporal network in supporting complex grammatical computations. Critically, they also point to the capacity of bilateral temporal regions to support simple, linear grammatical computations. This is consistent with a dual neurobiological framework where phylogenetically older bihemispheric systems form part of the network that supports language function in the modern human, and where significant capacities for language comprehension remain intact even following severe left hemisphere damage.