The objective of the present investigator-initiated mono-center trial to be performed at the Department of Neurology of the University Hospital Zurich is a detailed characterization of the effects of prolonged-release fampridine on walking function of 50-70 patients with MS. In a randomized, double-blind, placebo-controlled study with cross-over design, changes of essential gait elements such as stability, coordination, correct loading, posture or endurance in addition to walking speed after treatment with prolonged-release fampridine will be investigated using a comprehensive kinematic gait analysis protocol. This protocol comprises outcome parameters ranging from very specific and sensitive biomechanical measures to clinically meaningful indicators of improved ambulatory function. Kinematic, kinetic and electromyographic gait parameters will be assessed during treadmill walking (primary outcome parameters). Changes in overground walking capacity will be investigated by means of different functional walking tests (e.g. six minute walk test). Furthermore, the patient's perception of the effects of the treatment on walking function will be evaluated by a standardized questionnaire. Changes of global ambulatory activity will be assessed (Actimeter) indicating a successful translation of improved gait (sub-)functions due to prolonged-release fampridine treatment into everyday life. The study will last for a period of 18 weeks, excluding the screening period. Based on the mechanism of action, the investigators hypothesize that treatment with prolonged-release fampridine will not only improve walking speed, but also clinically more meaningful features of walking function in patients with MS.