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We report combined magnetic susceptibility,dielectric constant,nuclear quadruple resonance (NQR),and zero-field nuclear magnetic resonance (NMR) measurements on single crystals of multiferroics CuBr2.High quality of the sample is demonstrated by the sharp magnetic and magnetic-driven ferroelectric transition at TN =Tc ≈ 74 K.The zero-field 79Br and 81Br NMR are resolved below TN.The spin-lattice relaxation rates reveal charge fluctuations when cooled below 60 K.Evidences of an increase of NMR linewidth,a reduction of dielectric constant,and an increase of magnetic susceptibility are also seen at low temperatures.These data suggest an emergent instability which competes with the spiral magnetic ordering and the ferroelectricity.Candidate mechanisms are discussed based on the quasi-one-dimensional nature of the magnetic system.