As is well known, at low temperatures (around 10 mK) two-level systems (TLS’s) are responsible for the dipole echo phenomenon in glasses.  The magnetic field dependence of the echo amplitude is related to quadrupole electric moments of  non-spherical tunneling nuclei and/or magnetic dipole-dipole interaction of their nuclear spins. As a result TLS’s transform to multi-level systems with fine level splitting depending on magnetic field. These systems have new properties as compared to usual TLS’s and, in particular, exhibit oscillations of electric dipole echo amplitude in magnetic field.  We built a theory of this phenomenon and an excellent agreement of the theory with the experimental data has been obtained.