The layered oxides, Li0.5-xN1+xO2 with x similar or equal to 0.01 and 0.05, were synthesized by electrochemical deintercalation, and their structures were determined using TOF neutron diffraction measurements. Li0.5-xNi1+xO2 with x similar or equal to 0.01 has monoclinic symmetry and Li0.5-xNi1+xO2 with x similar or equal to 0.05 has rhombohedral symmetry; the reason for the lower symmetry of the structure with a slightly disordered Ni arrangement is discussed on the basis of the neutron diffraction results.