The structures of NaCuO2 and KCuO2 have been refined from time-of-flight neutron data. NaCuO2 is monoclinic: space group C2m, a = 6.3512(2)Å, b = 2.7474(1)Å, c = 6.1027(2)Å, β = 120.767(2)° with CuO = 1.839(1) Å (4×). KCuO2 is orthorhombic: space group Cmcm, a = 4.3742(1)Å, b = 11.6859(4)Å, c = 5.4124(2)Å with CuO = 1.826(3) Å (2×) and 1.832(2) Å (2×). Both structures contain strings of edge-sharing CuO4 rectangles. The sodium atoms center octahedra and the potassium atoms center trigonal prisms. Aspects of the crystal chemistry of both compounds are discussed.