Inclusion Criteria:  18-80 years of age Unilateral or bilateral lower limb amputation resulting in residual limb pain and/or phantom pain, fulfilling the criteria for definite neuropathic pain Usual pain intensity at least 4/10 over the past 24 hrs using the numerical scale of the BPI at screening Daily pain Pain for at least 3 months Stable pharmacological treatment for pain or no pharmaceutical treatment at least 1 month prior to the study Patients who can be followed for the whole duration of the study Minimum 4/10 pain intensity at the time of spinal anaesthesia for sub-study 1  Exclusion Criteria:  Any clinically significant or unstable medical or psychiatric disorder Subjects protected by law (guardianship or tutelage measure) History of or current substance abuse (alcohol, drugs) Pending litigation Contraindications to spinal anaesthetic block (e.g. use of prescribed or non-prescribed medication that can increase risk of bleeding such as anticoagulants, non-steroidal anti-inflammatory drugs and acetylsalicylic acid) Contraindication to rTMS (past severe head trauma, history of epilepsy or ongoing epilepsy, active cerebral tumour, past neurosurgical intervention, intracranial hypertension, implanted devices not compatible such as cardiac pacemaker and neurostimulator, cochlear implants, pregnancy or lactation. All women of childbearing age will be required to have negative pregnancy test at inclusion and to be using contraception) Other pain conditions more severe than phantom and residual limb pain. Inability to understand the protocol or to fill out the forms Other ongoing research protocol or recent past protocol within one month before the inclusion