The success of breakthrough projects and programs depends on two groups of factors: (i) the competence of organisations in managing of this projects and programs; (ii) "Entrepreneurial spirit (energy)" that is formed by the leadership of the organisation successful completion of the breakthrough projects. The success of the breakthrough project, as a management category, has contradictions which are formed as a result of different views of the interested parties. Thus, each of the key interested party has its level of competence in project management and may have opposing views on the success of the projects and their products and a new benchmark. The entrepreneurial energy of various interested parties promoting the breakthrough project contains contradictions which are to be accounted for by the organisation's leadership and emotion intelligence in project management processes. Entrepreneurial energy depends on "entrepreneurial capability" available in the organisation and the key interested parties. It is a set of orientations for success, individual and collective responsibility, cognitive capability, Emotion intelligence, freedom of expression and creativity. Entrepreneurial capabilities are a socio-determined set of features for organising and operating a business, which entrepreneurs could possess. The business often breakthrough capabilities are characterized by such properties as efforts to promote innovations, forms of implementation of the role function, the final product of economic creativity, ability to take risks, creativity, leadership ability as an entrepreneur, and individual psychological characteristics of the entrepreneur as management skills, independence in the selection and decision-making ability to respond to changes in the economic and social situation. Summing up all these definitions in the category of breakthrough concepts and tools for project management, we should note that the entrepreneurial capabilities determine the maturity or organisational competence in the management of projects, programs and portfolios of projects.