This paper presents robot-based Cyber-Physical System (CPS) for lan-guage therapy for children with communication disorders that was created and experimented in frame of the CybSPEED H2020-MSCA-RISE project. The CPS includes humanoid and semi-humanoid robots and is based on a combination of the best of experience, achievements and practices of the researchers from the domains of robotics, AI, system science and speech therapists. All experiments were conducted in accordance with the experimental protocol for measuring of listening, understanding and speaking skills for the verbal language in children with communication disorders, approved by the Ethics Committee for Scientific Research (ECSR) of the IR-BAS. In the paper, detailed description of the CPS, the organisation and conduction of the experiments are given. The first published results are commented which confirm the effectiveness of the robots - based CPS for the children with communication disorders.