In order to elucidate the effect of Ni ions in the Li layer on magnetism and Li diffusion of LiNiO 2 , we have measured muon-spin rotation and muon-spin relaxation ͑ + SR͒ spectra for the polycrystalline Li 1−x Ni 1+x O 2 samples with x = 0.02, 0.03, and 0.15. Weak transverse-field-+ SR measurements demonstrated the existence of a bulk ferromagnetic transition at T m =48͑6͒ K for the x = 0.03 sample and 161͑7͒ K for x = 0.15 while the x = 0.02 sample exhibited an antiferromagnetic transition at 18͑4͒ K. Zero-magnetic-field-͑ZF͒ + SR measurements below T m clarified the formation of static ferromagnetic ͑FM͒ order for the x = 0.03 and 0.15 samples but only a highly disordered antiferromagnetic ͑AF͒ order for the x = 0.02 sample. Therefore, the variation in the low-T magnetism with x is most unlikely due to the change in the concentration of an AF NiO-type domain or an FM Ni-rich cluster but likely due to a homogeneous change in the whole system. In the paramagnetic state, ZF-and longitudinal-field-+ SR spectra exhibited a dynamic nuclear field relaxation. From the temperature dependence of the field fluctuation rate, a diffusion coefficient of Li + ions ͑D Li ͒ at 300 K was estimated about 0.39͑3͒ ϫ 10 −11 cm 2 / s for the x = 0.02 sample and 0.12͑7͒ ϫ 10 −11 cm 2 / s for x = 0.15. On the other hand, the related compound, LiCrO 2 , did not show any diffusive behavior even at the highest temperature measured ͑=475 K͒. Considering the hindrance of diffusion by Ni in the Li + diffusion plane and the fact that LiCrO 2 is electrochemically inactive, the estimated D Li is thought to be very reasonable for the positive electrode material of Li-ion batteries. Furthermore, at low temperatures where the Li + ions are static, the internal magnetic field was still found to be fluctuating, due to a dynamic local Jahn-Teller distortion of the Ni 3+ ions in a low-spin state with S =1/ 2͑t 2g 6 e g 1 ͒.