[en] Difficulty and importance of determining possibility of occurrence of criticality in the accidents with destruction and even melting of nuclear fuel at NPP differ significantly whether this determination occurs immediately or after a long period of time since accident. Immediately after the accident, when situation is not yet stabilized, there is no sufficient amount of data on the state of fuel and moderator and this requires additional efforts to assembly conservative computational models. Current report presents an analysis of the experience of evaluations of criticality that were performed at the Kurchatov Institute immediately after accidents at the 4. block of the Chernobyl NPP in 1986, in the fuel assembly washing tank at the Paks NPP in 2003 and at the Fukushima NPP in 2011. Based on the experience of the first two accidents, there was developed the specialized complex SAPFIR-2006, designed for evaluation the criticality in severe beyond design basis accidents. The operative criticality evaluations made by this complex during the course of the accident did not significantly differ from the conclusions of subsequent analyzes performed quite a long time after the accident. However, earlier criticality evaluations may influence the management of the accident progression and the determination of optimal strategy of emergency response. After the accident at the Paks NPP, results of computational evaluation of the criticality were taken into account when preserving the subcritical state of tank with destroyed fuel and when removing fragments of fuel assemblies from the tank. In emergency response during Chernobyl accident, such results were not taken into account. In the accident at the Fukushima NPP, there was no opportunity to inform emergency workers with results of computational evaluation of the criticality. (authors)