The goal of this clinical trial is to learn if the drug called rituximab causes remission in patients with chronic inflammatory demyelinating polyneuropathy (CIDP). The aim is to investigate this in two types of patients, those who are newly diagnosed, and those who are already being treated and are dependent on the current standard therapy: immunoglobulins administered through infusion (IVIg) or through injection (SCIg). The main questions this trial aims to answer are: * To assess the effectiveness of rituximab * Whether it is possible and useful to prescribe patients rituximab who experience a relapse after at least six months after their last rituximab treatment. Participants will: * Receive the drug rituximab twice at the beginning of the trial and one additional time at six months. * The newly diagnosed patients will also start another treatment called IVIg, which a nurse will administer every three weeks during the first three to six months. * The patients who already being treated, will continue their regular treatment, until this is slowly reduced and stopped, during months three to six. * Visit the clinic over the course of two years, during which they will have approximately 10 visits, for checkups and tests. * Be asked to fill in questionnaires at each visit, and be asked to have their blood drawn four times.