This Phase 2a, multicenter, open-label safety and efficacy study will be performed at 3 sites in the United States. The study will enroll up to 38 subjects with nonsense mutation Duchenne muscular dystrophy who participated in a previous Phase 2a study of ataluren (Protocol Number PTC124-GD-004-DMD). Subjects will receive study drug 3 times per day (at breakfast, lunch, and dinner) for approximately 96 weeks (approximately 2 years). Study assessments will be performed at clinic visits during screening, every 6 weeks for the first 24 weeks, and then every 12 weeks until the end of the study. Additional safety laboratory testing, which may be performed at the investigational site or at an accredited local laboratory or clinic, is required every 3 weeks for the first 24 weeks and then every 6 weeks from Week 24 to Week 48. Subjects will have a biceps muscle biopsy before ataluren treatment and again after 24 weeks of ataluren treatment to evaluate changes in muscle dystrophin expression. An evaluation of the effects of ataluren on corticosteroid pharmacokinetics will be performed. Associated with this ataluren clinical trial is a substudy that will use magnetic resonance evaluations to assess changes in the composition of muscles of the legs.