Abstract. According to NOAA space weather scales, geomagnetic storms of scales G5 (3-h index of geomagnetic activity K p =9), G4 (K p =8) and G3 (K p =7) are dangerous for satellites, aircrafts, and even for technology on the ground (influence on power systems, on spacecraft operations, on HF radio-communications and others). We show on the basis of statistical data, that these geomagnetic storms, mostly accompanied by cosmic ray (CR) Forbush-decreases, are also dangerous for people's health on spacecraft and on the ground (increasing the rate of myocardial infarctions, brain strokes and car accident road traumas). To prevent these serious damages it is very important to forecast dangerous geomagnetic storms. Here we consider the principles of using CR measurements for this aim: to forecast at least 10-15 h before the sudden commencement of great geomagnetic storms accompanied by Forbush-decreases, by using neutron monitor muon telescope worldwide network online hourly data. We show that for this forecast one may use the following features of CR intensity variations connected with geomagnetic storms accompanied by Forbush-decreases: 1) CR pre-increase, 2) CR pre-decrease, 3) CR fluctuations, 4) change in the 3-D CR anisotropy.