Real-time language comprehension is a principal cognitive ability and thereby relates to central properties of the human cognitive architecture. Yet how do the presumably universal cognitive and neural substrates of language processing relate to the astounding diversity of human languages (over 5,000)? The authors present a neurocognitive model of online comprehension, the extended argument dependency model (eADM), that accounts for cross-linguistic unity and diversity in the processing of core constituents (verbs and arguments). The eADM postulates that core constituent processing proceeds in three hierarchically organized phases: (1) constituent structure building without relational interpretation, (2) argument role assignment via a restricted set of cross-linguistically motivated information types (e.g., case, animacy), and (3) completion of argument interpretation using information from further domains (e.g., discourse context, plausibility). This basic architecture is assumed to be universal, with cross-linguistic variation deriving primarily from the information types applied in Phase 2 of comprehension. This conception can derive the appearance of similar neurophysiological and neuroanatomical processing correlates in seemingly disparate structures in different languages and, conversely, of cross-linguistic differences in the processing of similar sentence structures.