Fludarabine and cyclophosphamide are designed to enter CLL cells and destroy the "machinery" that allows CLL cells to multiply. Rituximab is designed to bind to CLL cells and cause cell death. GM-CSF is designed to help the bone marrow to produce white cells. It may also increase the target molecule called cluster of differentiation antigen 20 (CD20) for rituximab on the surface of the CLL cells which may improve the activity of rituximab.