The compounds Sm3RuO7 and Eu3RuO7 were grown as singlecrystals from molten hydroxide fluxes. They crystallize in the orthorhombic space group Cmcm and are part of a well-known family of fluorite-related oxides of stoichiometry Ln(3)MO(7). This structure contains rare earth cations in two different coordination environments, 8-fold pseudocubic and 7-fold pentagonal bipyramidal, and contains Ru(V) cations that are octahedrally coordinated. The RuO6 octahedra are trans vertex-sharing to yield chains oriented along the c-axis. Upon cooling, single crystals of Sm3RuO7 and Eu3RuO7 undergo a structural transition at 190 and 280 K, respectively, from space group Cmcm to P2(1)nb. The structure transition results in a loss of lattice centering, a doubling of the b-axis, a distortion of the vertex-shared Ru-O chains, and a reduction in the coordination of one of the rare earth cations from 8-fold to 7-fold. Accompanying this structural transition are anomalies in the magnetic susceptibility at about 190 and 280 K for Sm3RuO7 and Eu3RuO7, respectively. The structures of these low-temperature phases of Ln(3)RuO(7) have been determined for the first time and are described.