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Experimental results on fast neutron generation in D(d,n) 3 He and T(d,n) 4 He reactions in the SOKOL-P laser facility are presented. Solid targets were irradiated by 1.054 μm, s-or ppolarized laser pulses of energy 5-8 J on target and duration 0.85-2 ps. The peak laser intensity was 0.5-2⋅10 18 W/cm 2 . Flat deuterated plastic (CD 2 ) n targets and TiD 0.5 T 0.5 targets were used in experiments. Some experiments were carried out with additional targets placed in front of and behind the laser target. The used time-of-flight technique helped identify neutrons from D(d,n) 3 He and T(d,n) 4 He reactions. Yields up to 10 6 DD-neutrons and 10 7 DT-neutrons were measured. Interaction of the fast ion beam with the target can explain the observed yield.