Language comprehension engages a cortical network of left frontal and temporal regions. Activity in this network is language-selective, showing virtually no modulation by nonlinguistic tasks. In addition, language comprehension engages a second network consisting of bilateral frontal, parietal, cingulate, and insular regions. Activity in this "Multiple Demand (MD)" network scales with comprehension difficulty, but also with cognitive effort across a wide range of non-linguistic tasks in a domain-general fashion. Given the functional dissociation between the language and MD networks, 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 assumed -implicitly or explicitly -that both networks track linguistic input closely, and in a manner consistent across individuals. Here, we used fMRI to directly test this assumption by comparing the BOLD signal time-courses in each network across different people listening to the same story. 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.Significance Statement: Language comprehension recruits both language-specific mechanisms and domain-general mechanisms that are engaged in many cognitive processes. In the human cortex, language-selective mechanisms are implemented in the left-lateralized "core language network", whereas domain-general mechanisms are implemented in the bilateral "Multiple Demand (MD)" network. Here, we report the first direct comparison of the respective contributions of these networks to naturalistic story comprehension. Using a novel combination of neuroimaging approaches we find that MD regions track stories less closely than language regions. This finding constrains the possible contributions of the MD network to comprehension, contrasts with accounts positing that this network has continuous access to linguistic input, and suggests a new typology of comprehension processes based on their extent of input tracking.peer-reviewed)