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One out of two multiple sclerosis patients is cognitively impaired and this impairment has a profound impact on the patient’s daily life. The treatment of cognitive impairment is an important unmet need in multiple sclerosis. There is promising evidence for positive results after cognitive rehabilitation programs, but methodological difficulties hamper definite conclusions on the subject. Recently there has been interest in the association between cognition and physical performance and there is promising evidence for the possibility of enhancing cognition by training and improving physical performance and vice versa. Our goal is to perform a randomized sham controlled clinical trial with a cognitive-motor rehabilitation program for cognitively impaired patients with multiple sclerosis that can be safely carried out at the patient’s home and that improves both working memory and information processing speed, with walking performance as a secondary endpoint. We will identify possible mechanisms of cognitive improvement by analysing changes on structural MRI and resting-state and task-related EEG before and after rehabilitation. Finally, we will reveal factors that can predict response to the rehabilitation program.