  The GRT modification taking into account the dependence of metric on the
velocities of the sources is built. It is shown that this dependence follows
from the equivalence principle and from the inseparability of the field
equations and geodesics equations. As it is known, the latter are the
conditions of the field equations solvability, and their form coincides with
Newtonian one only in the lowest approximation. The obtained modification
provides the explanation for the flat character of the rotation curves of
spiral galaxies, for Tully-Fisher law, for some specific features of globular
clusters behavior and for the essential excess of the observable gravitational
lens effect over the predicted one. Neither dark matter nor arbitrary change of
dynamics equations appeared to be needed. Important cosmological consequences
are obtained.
