Children with Specific Language Impairment (SLI) have been observed to have production and perception difficulties with sentences containing long-distance dependencies, but it is unclear whether this is due to impairment in grammatical knowledge or in processing mechanisms. The current study addressed this issue by examining automatic on-line gap-filling in relative clauses, as well as off-line comprehension of the same stimulus sentences. As predicted by both knowledge impairment and processing impairment models, SLI children showed lack of immediate gap-filling after the relative clause verb, in comparison to a control group of typically developing children. However, on the off-line measure of comprehension of the same stimuli sentences, SLI children and TD children did not differ qualitatively. This finding is incompatible with knowledge impairment. We interpret the results to show that SLI children have impaired processing mechanisms (such as temporally delayed gap-filling) but are not impaired in their grammatical knowledge.