This study explored the notion that the extent to which language-impaired children can become bilingual depends on the type of language impairment. Single-case studies were conducted on two 7-year-old bilingual children, who had both been exposed to English and Afrikaans consistently and regularly from an early age. The subjects presented with specific language impairment (SLI) and semantic-pragmatic disorder (SPD), respectively. They were assessed on a battery of cognitive and linguistic tests in both their languages. Results indicate that the SLI subject, who presented with a deficit in successive processing on the Cognitive Assessment System, had difficulty in acquiring the surface features of both languages. She developed much better proficiency in English than in Afrikaans, despite substantial exposure to the latter. The SPD subject, whose cognitive profile was characterised by planning and attention deficits, but a strength in successive processing, presented with equal proficiency in both languages. The theoretical and clinical implications of this research are discussed.