Thematic-role assignment is influenced by several classes of cues during sentence comprehension, ranging from morphological exponents of syntactic relation such as case and agreement to probabilistic cues such as prosody. The effect of these cues cross-linguistically varies, presumably reflecting their language-specific robustness in signaling thematic roles. However, language-specific frequencies are not mapped onto the cue strength in a one-to-one fashion. The present article reports two eye-tracking studies on Hungarian examining the interaction of case and prosody during the processing of case-unambiguous (Experiment 1) and case-ambiguous (Experiment 2) clauses. Eye fixations reveal that case is a strong cue for thematic role assignment, but stress only enhances the effect of case in case-unambiguous clauses. This result differs from findings reported for Italian and German in which case initial stress reduces the expectation for subject-first clauses. Furthermore, the sentence comprehension facts are not explained by corpus frequencies in Hungarian. After considering an array of hypotheses about the roots of cross-linguistic variation, we conclude that the crucial difference lies in the high reliability/availability of case cues in Hungarian in contrast to the further languages examined within this experimental paradigm.