Scientific and technical problems of accuracy improvement of stellar position measurements in the LOMONOSOV project are discussed. In contrast to the HIPPARCOS project, in our project we use a steerable satellite with a three-axis spatial stabilization. A Cassegrain-type 1-meter mirror telescope will be mounted on board of the satellite. We discuss scientific goals in astrophysics, stellar astronomy and astrometry, for which the knowledge of stellar positions with sub-milliarcsecond accuracy is necessary.