The "Prognoz" routine has been worked out at the Astronomical Council permitting high-accuracy prediction of artificial satellites´ motion in an interval of several days. Numerical integration of equations of the motion of artificial satellites was used; the geopotential and the point-mass model to substitute it, gravitational influence of the Moon and the Sun, solar pressure, the influence of solid Earth tides and upper atmosphere drag are also taken into acount. The routine can be used to improve orbital elements, station positions, determination of coordinates of the Earth Pole and instability of the Earth rotation. Using laser ranging data of Lageos, during preliminary MERIT campaign, an accuracy of less than 1 meter for orbital elements was obtained, pole positions and LOD were calculated for intervals of 2,5 to 5 days.