Based on development of the concept of the Triple Helix Model and models of the innovation process, an integration model for development of the innovation system of Ukraine and a model of the open innovation process are proposed. The development of the innovation system of Ukraine essentially depends on the implementation of open innovation processes of scientific organizations and enterprises of Ukraine are provided. The proposed "Six Helix Model" combines the innovative institutional members of the European Union and Ukraine (scientific organizations, universities, enterprises, state and public organizations). The model of open innovation process involves the use of subprocesses: outward inside, inside outward and connecting. Also, the indicators of evaluation and management of open innovation processes are proposed. The indicators for assessment and management of open innovation processes are proposed that allow participants to find innovative process: the new knowledge and ideas which are outside scientific organizations and enterprises; how to develop new competencies scientific organizations and businesses to use them in an open innovation process; new tools for access to finance and to reduce the entry of open innovation (products and technologies).