The processing of words containing inflectional affixes triggers morphophonological parsing and affix-related grammatical information processing. Increased perceptual complexity related to stem-affix parsing is hypothesized to create predominantly domain-general processing demands, whereas grammatical processing primarily implicates domain-specific linguistic demands. Exploiting the properties of Russian morphology and syntax, we designed an fMRI experiment to separate out the neural systems supporting these two demand types, contrasting inflectional complexity, syntactic (phrasal) complexity, and derivational complexity in three comparisons: (a) increase in parsing demands while controlling for grammatical complexity (inflections vs. phrases), (b) increase in grammatical processing demands, and (c) combined demands of morphophonological parsing and grammatical processing (inflections and phrases vs. derivations). Left inferior frontal and bilateral temporal areas are most active when the two demand types are combined, with inflectional and phrasal complexity contrasting strongly with derivational complexity (which generated only bilateral temporal activity). Increased stem-affix parsing demands alone did not produce unique activations, whereas grammatical structure processing activated bilateral superior and middle temporal areas. Selective left frontotemporal language system engagement for short phrases and inflections seems to be driven by simultaneous and interdependent domain-general and domain-specific processing demands.