Multiple sclerosis is disease believed to be due to immune cells, cells which normally protect the body, but are now attacking the tissue in the brain and possibly the spinal cord. The likelihood of progression of this disease is high. This study is designed to examine whether treating patients with high dose cyclophosphamide and CAMPATH-1H (drugs which reduce the function of the immune system) followed by return of previously collected blood stem cells will stop the progression of your multiple sclerosis. Stem cells are undeveloped cells that have the capacity to grow into mature blood cells, which normally circulate in the blood stream. The purpose of the cyclophosphamide and CAMPATH-1H is to destroy the cells in your immune system which are thought to be causing your disease. The purpose of the stem cell infusion is to restore the body's blood production, which will be severely impaired by the high dose chemotherapy and to produce a normal immune system that will no longer attack the body.