In this study, patients with hemophilia A or hemophilia B due to a nonsense mutation will be treated with an investigational drug called ataluren (PTC124). Evaluation procedures to determine if a patient qualifies for the study will be performed within 14 days prior to the start of treatment. Eligible patients who elect to enroll in the study will then participate in a 28-day treatment period. Within the 28-day period, ataluren (PTC124) treatment will be taken 3 times per day with meals for 14 days at a dose of 10 mg/kg (morning), 10 mg/kg (midday) and 20 mg/kg (evening); there will then be an interval of approximately 14 days without treatment. During the study, ataluren (PTC124) efficacy, safety, and pharmacokinetics will be evaluated periodically with measurement of FVIII/FIX activity and inhibitor levels, other blood tests, and urinalysis.