The study of migrating seismicity was carried out according to data on 52700 earthquakes of representative energy classes KР ≥ 8, which occurred in the lithosphere of the Baikal Rift Zone (BRZ) from 1964 to 2013. M = 2143 quasilinear chains of earthquakes are distinguished and the basic laws of the space-time and energy distribution are established. In the epicentral field of the BRZ seismicity, there are chains of “seismic migration” and chains formed by chance (“pseudo-migration”). To identify the migrating seismicity, the seismic migration activity index (ISMA) was used, which characterizes the seismic migration / pseudo-migration ratio at a given level of significance, obtained maps of the distribution of the index over the territory and graphs of changes over years. The results of the study indicate a direct link between the migrating BRZ seismicity and the location and activation of rifting attractor structures (RAS).