Patients with multiple sclerosis who have had at least one relapse within 18 months of the start of the study and in whom interferon-beta treatment has not been successful may be considered for this study. There are two study phases: baseline and treatment. During the baseline phase, patients will have three magnetic resonance imaging (MRI) scans over 2 months to evaluate their disease activity. During treatment, patients will receive seven intravenous (I.V.) infusions of Zenapax in the clinic. The first two infusions will be given 2 weeks apart; the next five will be given once a month.