The subsolidus phase relations of R 2 O 3 -CaO-CuO ternary systems (R=Nd, Sm, Gd, Tm) have been investigated by X-ray powder diffraction. All samples were synthesized at about 950 o in air. There exists a ternary compound Ca 1 4 - x R x Cu 2 4 O 4 1 (x = 4 for R=Nd, Gd and x = 5 for R = Sm) and a ternary solid solution Ca 2 + x R 2 - x Cu 5 O 1 0 (R=Nd, Sm, Gd, Tm) with a wide composition range Δx of about 0.6. The compound Ca 1 4 - x R x Cu 2 4 O 4 1 possesses a layered orthorhombic structure and is isostructural to Sr 1 4 - x Ca x Cu 2 4 O 4 1 . The lattice parameters a and c of the compound are basically independent of the ionic radius of R, while the lattice parameter b and unit-cell volume V decrease substantially with the decrease of the ionic radii of R. The Ca 2 + x R 2 - x Cu 5 O 1 0 solid solution is isostructural to Ca 2 + x Y 2 - x Cu 5 O 1 0 , the structure of which is based on an orthorhombic ''NaCuO 2 -type'' subcell containing infinite one-dimensional chains of edge-shared square planar cuprate groups crosslinked by the layered cations Ca and R that locate in the inter-chain tunnels.