The question of prediction and prevention of dynamic events - rock bursts (RB), tectonic rock burst (TRB) and mining-induced earthquakes (MIE), induced by large-scale mining, are discussed. The mine itself and the host geological environment are taken as a natural-technical system (NTS) whose evolution is characterised by alteration of the adaptation-bifurcation (catastrophes) periods. So, to predict TRB-MIE means to predict the limiting NTS states that are determined from the NTS geological monitoring data, and to prevent the said events means to control the processes of rock deformation and failure within the critical zone. The study considers particular examples of how TRB-MIE-events are predicted and prevented in apatite mines, Kola peninsula, Russia.