DMD/BMD is a genetic disorder that develops in boys. It is caused by a mutation in the gene for dystrophin, a protein that is important for maintaining normal muscle structure and function. Loss of dystrophin causes muscle fragility that leads to weakness and loss of walking ability during childhood and teenage years. A specific type of mutation, called a nonsense (premature stop codon) mutation is the cause of DMD/BMD in approximately 13 percent (%) of boys with the disease. Ataluren is an orally delivered, investigational drug that has the potential to overcome the effects of the nonsense mutation. This study is a Phase 2b trial that will evaluate the clinical benefit of ataluren in boys with DMD/BMD due to a nonsense mutation. The main goals of the study are to understand whether ataluren can improve walking, activity, muscle function, and strength and whether the drug can safely be given for a long period of time.