  The effect of a magnetic field on the dipole echo amplitude in glasses at
temperatures of about 10 mK caused by nonspherical nuclei with electric
quadrupole moments has been studied theoretically. It has been shown that in
this case, the two-level systems (TLS's) that determine the glass properties at
low temperatures are transformed into more complicated multilevel systems.
These systems have new properties as compared to usual TLS's and, in
particular, exhibit oscillations of electric dipole echo amplitude in magnetic
field. A general formula that describes the echo amplitude in an arbitrary
split TLS has been derived with perturbation theory. Detailed analytic and
numerical analysis of the formula has been performed. The theory agrees
qualitatively and quantitatively well with experimental data.
