This is a multicenter, prospective, randomized, open-label efficacy and safety study. The study is being done to see whether treatment using Pegasys (pegylated interferon alfa-2a) and Copegus (ribavirin) is safer and more effective in liver transplant recipients when given before hepatitis C infection reappears, or when it is given after clinical symptoms of hepatitis C reinfection appear. The study is also being done in liver transplant recipients to estimate how much hepatitis C is detected over time, how the body affects the study drugs, the safety of the study drugs whether or not the study drugs effect the participants' quality of life, and whether or not the participants feel more or less depressed as a result.