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One of the safety problems of the next-step fusion device 'International Thermonuclear Experimental Reactor' (ITER) is the explosion hazard of the dusts produced as a result of plasma-wall interaction. In case of air ingress inside the vacuum vessel, dusts can be mobilized forming an explosive cloud.To evaluate the explosion hazard of ITER-relevant dusts, a standard method of 20-l-sphere was used to measure the explosion indices of fine graphite and tungsten dusts and their mixtures. The effect of dust particle size was studied on the maximum overpressures, maximum rates of pressure rise, and lower explosive concentrations of graphite dusts in the range 4 to 45 micrometers. The explosion indices of 1 micrometer tungsten dust and its mixtures with 4 micrometers graphite dust were measured. The explosibility of these dusts and mixtures were evaluated. The dusts tested were ranked as Stl class. Dust particle size was shown to be very important for explosion properties. The finest dust had the lowest minimum explosion concentration (70 g/m3) and, as distinct from coarser graphite dusts, it exploded with 2 kJ ignition energy. Tungsten dust of 1 micrometer characteristic particle size was able to explode in a wide range of concentrations.