Purpose: The hypothesis that the linguistic deficit presented by children with specific language impairment (SLI) is caused by limited cognitive resources (e.g., S. Ellis Weismer & L. Hesketh, 1996) was tested against the hypothesis of a limitation in linguistic knowledge (e.g., M. L. Rice, K. Wexler, & P. Cleave, 1995). Method: The study examined the influence of the argument-structure complexity of a target sentence on the production of grammatical morphemes in French children with SLI compared with younger children matched for grammatical level in production (GL) and children of the same chronological age (CA). A sentence production task was used where the target sentences varied in terms of argument complexity and length. Results: The results indicated that children with SLI used articles and auxiliaries in obligatory contexts significantly less often than both the GL and CA control groups: More complex argument structures elicited the highest number of grammatical morpheme omissions; this effect was larger in children with SLI than in the GL group and was independent of the length of the sentences, which failed to show any influence on the production of grammatical morphemes. Conclusion: These results support the hypothesis that grammatical-morpheme deficit in SLI depends at least in part on limited processing capacities.