Language comprehension engages a cortical network of left frontal and temporal regions [1-6]. Activity in this network is sensitive to linguistic features such as lexical information, syntax and compositional semantics [7-10]. However, this network shows virtually no engagement in non-linguistic tasks [11-14] and is therefore language-selective. In addition, language comprehension engages a second network consisting of frontal, parietal, cingulate, and insular regions [15-18]. Activity in this "Multiple Demand (MD)" network  is sensitive to comprehension difficulty, increasing in the presence of e.g. ambiguity [20-26], infrequent words [27-33] and non-local syntactic dependencies [34-40]. However, this network similarly scales its activity with cognitive effort across a wide range of non-linguistic tasks [19, 41] and is therefore domain-general. Given the functional dissociation between the language and MD networks [42, 43], their respective contributions to comprehension are likely distinct, yet such differences remain elusive. Critically, given that each network is sensitive to some linguistic features, prior research has presupposed that both networks track linguistic input closely, and in a manner consistent across individuals. Here, we used fMRI to test this assumption by comparing the BOLD signal time-courses in each network across different individuals listening to the same story [44-46]. Language network activity showed fewer individual differences, indicative of closer input tracking, whereas MD network activity was more idiosyncratic and, moreover, showed lower reliability within an individual across repetitions of a story. These findings constrain cognitive models of language comprehension by suggesting a novel distinction between the processes implemented in the language and MD networks.