The presented contribution is a brief summary of the knowledge obtained working on Project of development and utilization of science and technology in SR up to 2015. The summary contains results reached by the use of the methodological procedure of Technology Foresight. The content of the contribution is a brief characteristic of the used methodology of prognosis of the trends of science and technology. In Slovakia, its development is regarded as a priority in the context of competitiveness of the Slovak economy, its sustainable growth, social development, improvement of environmental quality, as well as improvement of competitiveness of science and technology in Slovakia with that of Europe. The contribution also includes proposals of system priorities necessary for successful development and use of suggested trends of science and technology.