This paper reports on the preparation of Li5ReOr, Li4NpO5 and LisNpO6 by solid-state reactions, the results of X-ray and neutron powder diffraction measurements on all three compounds, and the determination of the structures of Li5ReO6 and Li,NpO5 from the neutron data. The neutron powder diffraction refinement for LisReO6 confirms a recent single-crystal X-ray diffraction study: monoclinic, space group C2/m. This structure is retained by LisReO6 between 298 K and 10 K. The neutron powder diffraction refinement for Li4NpO5 confirms earlier X-ray powder diffraction results: tetragonal, space group I4/rn, a = 6.698/~, c = 4.415 /~. The lithium and oxygen positional parameters of Li4NpO5 have been refined: coordination about Np is an extended octahedron, with each Np ion surrounded equatorially by four oxygen ions at 2.00 ~ and axially by two oxygen ions at 2.21 ~. Li5NpO6 shows an X-ray powder pattern consistent with the original report, but the neutron diffraction data set could not be refined in terms of the originally proposed space group or any other plausible model structure.