Masitinib is a selective tyrosine kinase inhibitor that is thought to exert a neuroprotective effect through its activity on mast cells and other non-neuronal cells of the central nervous system, with subsequent modulation of inflammatory and neurodegenerative processes. The objective of this study is to compare the efficacy and safety of masitinib at 4.5 mg/kg/day versus matched placebo, or masitinib at 4.5 mg/kg/day with a dose escalation to 6 mg/kg/day after 3 months of treatment versus matched placebo, in the treatment of patients with primary progressive multiple sclerosis or relapse-free secondary progressive multiple sclerosis. Approximately 600 patients will be randomized into four treatment groups with a 2:2:1:1 design. The primary outcome measure is the Expanded Disability Status Scale (EDSS) after 96 weeks of treatment in the overall study population with subgroup analysis performed in stratum (primary progressive multiple sclerosis / secondary progressive multiple sclerosis).