The primary goal of this study is to evaluate the efficacy of Enbrel in patients with primary systemic amyloidosis using a one-stage, phase II study design with an interim analysis. This study will also assess survival and progression times, symptom relief, and toxicity associated with Enbrel in primary systemic amyloidosis patients. Two groups of patients with very different risk profiles can be identified with respect to this disease. Patients with symptomatic cardiac disease and/or at least two involved organs ar at high risk and historically have a median survival less than six months. Patients without these conditions have a significantly better prognosis. Both subgroups will be studied in the present study, and essentially two phase-II clinical trials, one for each subgroup, will be run in parallel.