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Magnetic correlations in superconducting LiFeAs were studied by elastic and by inelastic neutron scattering experiments. There is no indication for static magnetic ordering but inelastic correlations appear at the incommensurate wave vector (0.5 ± δ, 0.5 ∓ δ, 0) with δ ∼0.07 slightly shifted from the commensurate ordering observed in other FeAs-based compounds. The incommensurate magnetic excitations respond to the opening of the superconducting gap by a transfer of spectral weight.PACS numbers: 74.25. Ha,74.25.Jb,78.70.Nx,75.10.Lp Superconductivity in the FeAs-based materials [1] appears to be closely related to magnetism as the superconducting state emerges out of an antiferromagnetic phase by doping [1][2][3][4] or by application of pressure [5]. The only FeAs-based exception to this behavior has been found in LiFeAs, which is an ambient-pressure superconductor with a high T C of ∼17 K without any doping [6][7][8]. LiFeAs exhibits the same FeAs layers as the other materials but FeAs 4 tetrahedrons are quite distorted [8] suggesting a different occupation of orbital bands. Indeed ARPES studies on LiFeAs find an electronic band structure different from that in LaOFeAs or BaFe 2 As 2 type compounds [9]. The Fermi-surface nesting, which is proposed to drive the spin-density wave (SDW) order in the other FeAs parent compounds, is absent in LiFeAs [9] suggesting that this magnetic instability is less relevant. The main cause for the suppression of the nesting consists in the hole pocket around the zone center which is shallow in LiFeAs [10]. In consequence, there is more density of states near the Fermi level which might favor a ferromagnetic instability. Using a three-band model Brydon et al.[10] find this ferromagnetic instability to dominate and discuss the implication for the superconducting order parameter proposing LiFeAs to be a spin-triplet superconductor with odd symmetry. However, other theoretical analyzes of the electronic band-structure still find an antiferromagnetic instability which more closely resembles those observed in the other FeAs-based materials [11].Inelastic neutron scattering (INS) experiments revealed magnetic order and magnetic excitations in many FeAs-based families [2,[12][13][14]. Strong magnetic correlations persist far beyond the ordered state, and, most importantly, the opening of the superconducting gap results in a pronounced redistribution of spectral weight [13][14][15], which is frequently interpreted in terms of a resonance mode. Recently a powder INS experiment on superconducting LiFeAs reported magnetic excitations to be rather similar to those observed in the previously studied materials [16] but with a spin gap even in the normal-conducting phase. Magnetic excitations observed in a recent single-crystal INS study on nonsuperconducting Li deficient Li 1−x FeAs (x∼0.06) were described by spin-waves associated with commensurate antiferromagnetism, again with a large temperature independent spin gap of 13 meV [17]. We have performed INS experiments on superconducting sing...