The crystal structure of the C polymorph of the solid solutions, Li0.5−3x RE0.5+x TiO3 (RE = Pr, Nd) determined from powder neutron diffraction using Rietveld refinement, is an ordered perovskite of the GdFe03 type. The structures of both phases are similar: the A sites contain (0.5+x) RE cations and (0.5−3x) off-centre lithium ions, with 2x sites vacant. Orthorhombic unit cell, RE = Nd: a = 5.43661(7) Å, b = 7.6647(1) Å, c = 5.39752(7) Å; RE = Pr: a = 5.43793(5) Å, b = 7.66828(8) Å, c = 5.40769(5) Å; space group Pnma (no. 62). Conduction occurs by a Li+ vacancy mechanism through interconnecting A sites, avoiding those sites that are occupied by the RE cations.