The purpose of this research is to offer lamivudine treatment to patients who were participating in earlier lamivudine protocols and who did not maintain a response. This means that at the end of the study hepatitis B virus was still present in the blood. Also, researchers would like to gain information on the long term use of lamivudine in the treatment of hepatitis B infection. Lamivudine is an investigational medicine. Early studies in animals and in more that 850 patients with chronic hepatitis B infection have shown that it may inhibit or suppress hepatitis infection.