The article considers the problem of the development of soft skills of teachers of Physics and Mathematics in the system of postgraduate pedagogical education of Ukraine. The experience of foreign countries in general and the People’s Republic of China in particular on the relevant online and offline teachers’ course training has been analyzed, the essence and significance of such soft skills as sociability, creativity, empathy for the professional development of teachers of Physics and Mathematics has been characterized. The state of these skills development of teachers of Physics and Mathematics was studied, the average level of the development these skills has been stated. The possibilities of the development of soft skills were determined, the four-stage process of their transition from unconscious incompetence to unconscious competence in the system of postgraduate education was substantiated. The principles, forms, methods, technologies of the development of soft skills in the system of advanced training of teachers of Physics and Mathematics were discussed with the emphasis placed on the role of heuristic methods and forms, creative technologies of the development of soft skills.