[en] Experimental results on fast neutron generation in D(d,n)He³ and T(d,n)He⁴ reactions in the SOKOL-P laser facility are presented. Solid targets were irradiated by 1.054 μm, s- or p-polarized laser pulses of energy 5-8 J on target and duration 0.85-2 ps. The peak laser intensity was 0.5 - 2.10¹⁸ W/cm². Flat deuterated plastic (CD₂)_n targets and TiD_αT_β targets were used in experiments. Some experiments were carried out with additional targets placed in front of and behind the laser target. The used (TOF) time-of-flight technique helped identify neutrons from D(d,n)He³ and T(d,n)He⁴ reactions. Yields up to 10⁶ DD-neutrons and 10⁷ DT-neutrons were measured. Interaction of the fast ion beam with the target can explain the observed yield. (authors)