Background: The computational grammatical complexity (CGC) hypothesis claims that children with G(rammatical)-specific language impairment (SLI) have a domain-specific deficit in the computational system affecting syntactic dependencies involving 'movement'. One type of such syntactic dependencies is filler-gap dependencies. In contrast, the Generalized Slowing Hypothesis claims that SLI children have a domain-general deficit affecting processing speed and capacity. Aims: To test contrasting accounts of SLI we investigate processing of syntactic (filler-gap) dependencies in wh-questions. Methods & Procedures: Fourteen 10;2-17;2 G-SLI children, 14 age-matched and 17 vocabulary-matched controls were studied using the cross-modal picture-priming paradigm. Outcomes & Results: G-SLI children's processing speed was significantly slower than the age controls, but not younger vocabulary controls. The G-SLI children and vocabulary controls did not differ on memory span. However, the typically developing and G-SLI children showed a qualitatively different processing pattern. The age and vocabulary controls showed priming at the gap, indicating that they process wh-questions through syntactic filler-gap dependencies. In contrast, G-SLI children showed priming only at the verb. Conclusions: The findings indicate that G-SLI children fail to establish reliably a syntactic filler-gap dependency and instead interpret wh-questions via lexical-thematic information. These data challenge the Generalized Slowing Hypothesis account, but support the CGC hypothesis, according to which G-SLI children have a particular deficit in the computational system affecting syntactic dependencies involving "movement". As effective remediation often depends on aetiological insight, the discovery of the nature of the syntactic deficit, along side a possible compensatory use of semantics to facilitate sentence processing, can be used to direct therapy. However, the therapeutic strategy to be used, and whether such similar strengths and weaknesses within the language system are found in other SLI subgroups are empirical issues that warrant further research. The following are appended: (1) Individual performance of children with G-SLI for matching and selection; and (2) Verbs used in the cross-modal priming experiment. (Contains 4 tables and 8 notes.)