Inclusion Criteria:  Disease duration of 24 months or less and documented clinical worsening (clinical or ENMG or disability) over the past 12 months IgM gammopathy, either MGUS or Waldenstrom Macroglobulinemia (WM) Demyelinating polyneuropathy according to European Federation of Neurological Societies/Peripheral Nerve Society guidelines for chronic inflammatory demyelinating polyneuropathy on nerve conduction studies. Anti-MAG titre of 10 000 BTU or more Total INCAT score of 1 point or more at baseline Absence of immunoglobulin treatment within 3 months prior to inclusion. Absence of immunosuppressive therapy within 6 months prior to inclusion, including steroid therapy of 2 months or more as part of the management of neuropathy. Negative β-human chorionic gonadotropin (HCG) in women of childbearing potential Women of childbearing potential must agree to use contraception for 365 days following administration of rituximab.  Exclusion Criteria:  - Unable to give informed consent History of severe allergic or anaphylactic reaction to chimeric monoclonal antibody Hypersensitivity known to one of the compounds of polaramine or methylprednisolone Previous treatment with rituximab Diseases known to cause polyneuropathy (e.g. diabetes, uncontrolled thyroid disease, vitamin B1 or B12 deficiency, renal (GFR < 60ml ml/min/1,73 m2- Modification of Diet in Renal Disease (MDRD) formula) or liver disorder, myeloma, amyloidosis, cryoglobulinemia) Indication of specific immunosuppressive therapy for WM Significant uncontrolled disease at baseline such as cardiovascular (including cardiac arrhythmia), pulmonary (including obstructive pulmonary disease), renal, hepatic, endocrine or gastrointestinal or any other significant disease that may prevent patient from participating in the study Congestive heart failure (NYHA III or IV) Known active bacterial, viral, fungal mycobacterial infection History or known presence of recurrent or chronic infection (e.g. viral hepatitis, HIV syphilis, tuberculosis). History of cancer, including solid tumors and haematological malignancies (except basal cell and in situ squamous carcinoma of the skin, in situ carcinoma of the cervix of the uterus that have been excised and resolved, with documented clear margins on pathology) History of alcohol (more than two drinks a day for a woman, more than 4 glasses a day for a man [World Health Organization (WHO) definition]) or other drug abuse within 6 months prior to randomization History or currently active primary or secondary immunodeficiency White blood cell count < 1500/mm3 or platelet count < 75 000/mm3 Angle closure glaucoma, Urinary retention related to urethroprostatic disorders, Uncontrolled psychotic disorders, Severe liver failure, Recent vaccination with live vaccines (<3months) and vaccination with live virus vaccines is not recommended during the overall study period.