LEED crystallographic analyses have been made for two structures formed by the (0001) surface of zirconium and which show (1 × 1)-type diffraction patterns. An analysis with eight diffracted beams for clean Zr(0001) supports an earlier conclusion that this surface has a regular hcp-type structure, and that the first interlayer spacing shows a contraction from the bulk spacing by about 1.6%. A surface formed by O, at twice the coverage applying for the best-developed half-monolayer (2 × 2) diffraction pattern, is analyzed using tensor LEED for nine diffracted beams, including the use of the average t-matrix approximation. It is concluded that the 1 monolayer (ML) structure is actually disordered with 0.5 ML of O distributed statistically over octahedral holes between the first and second Zr layers, and another 0.5 ML of O similarily distributed between the second and third metal layers.