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The “break-junction” technique [1] exploited to make microcontacts in single-crystal samples of LiFeAs (bulk Tc = (10÷17) K), allows us to make clean cryogenically cleaved surfaces and to change constriction properties. In our investigation using Andreev superconductor – normal metal – superconductor-contacts (SNS) we observed two reproducible independent subharmonic gap structures at dynamic conductance characteristics. Intrinsic Andreev spectroscopy has been used to define namely bulk superconducting gaps energy that can be yielded directly from bias voltages of gaps peculiarities at any T < Tc [2]. From these results, we can derive the energy of the large superconducting gap Δ_L = (2.5 ÷ 3.4) meV and the small gap Δ_S = (0.9 ÷ 1) meV at T = 4.2 K for the Tc_local ≈ (10.5 ÷ 14) K (the contact area critical temperature which deviation causes the variation of Δ_L). The BCS-ratio is found to be 2Δ_L/kTc = (4.6 ÷ 5.6), whereas 2Δ_S/kBTC ≈ 1 << 3.52 results from induced superconductivity in the bands with the small gap. The authors are grateful to Prof. Ya.G. Ponomarev for providing techniques and materials. We also thank S.V. Borisenko and A.N. Vasiliev. This work was supported by RFBR-DFG (№10-03-91334), the MES of Russia (MK-3264.2012.2), the DFG (BE1749/13). [1] J. Müller et al., Physica C 191, 485 (1992). [2] R. Kümmel et al., Phys. Rev. B 42, 3992 (1990).