  The effect of a magnetic field on the dipole echo amplitude in glasses (at
temperatures of about 10 mK) induced by the dipole-dipole interaction of
nuclear spins has been theoretically studied. It has been shown that a change
in the positions of nuclear spins as a result of tunneling and their
interaction with the external magnetic field E_H lead to a nonmonotonic
magnetic field dependence of the dipole echo amplitude. The approximation that
the nuclear dipole-dipole interaction energy E_d is much smaller than the
Zeeman energy E_H has been found to be valid in the experimentally important
cases. It has been shown that the dipole echo amplitude in this approximation
may be described by a simple universal analytic function independent of the
microscopic structure of the two-level systems. An excellent agreement of the
theory with the experimental data has been obtained without fitting parameters
(except for the unknown echo amplitude)
