Spasticity is velocity and acceleration dependent, and it is therefore important to execute physiotherapeutic exercises at a relatively low and constant velocity. This can be more accurately managed by a robot than by a person when such exercises are administered continuously for more than 15–20 min. The purpose of this project was to construct a robot-mediated system that could support upper limb physiotherapy of patients with spastic hemiparesis. The system, unlike any known robotic therapeutic system, uses unmodified industrial robots to carry out passive physiotherapy on the upper limb (including the movements of the shoulder and the elbow). An initial trial was executed in order to assess its safety and to gain experience of the robot-mediated therapy. Four healthy subjects and eight patients with spastic hemiparesis were included. Each subject received 30-min-long robotic physiotherapy sessions over 20 consecutive workdays. The 12 participants received, in total, 240 robot-mediated physiotherapeutic sessions. No dangerous situation or considerable technical problem occurred; the robots executed the therapy programme as intended. Investigation of the effectiveness of this kind of therapy was not an aim of this initial trial; however, the patients’ clinical status was followed and some favourable changes were found regarding the spasticity of elbow flexors and shoulder abductors. According to the experiences of the first clinical investigation, the programming interface and the mechanical interface device between the patient and the robots had been improved. A controlled clinical study is under way to assess the effectiveness of the REHAROB movement therapy.