The crystallographic and physical properties of TbRuAsO and DyRuAsO at and below room temperature are reported, including full structure refinements from powder X-ray diffraction data and measured electrical and thermal transport properties, magnetic susceptibility, and heat capacity. Both compounds are isostructural to LaFeAsO (ZrCuSiAs-type, P4/nmm) at room temperature. However, DyRuAsO undergoes a symmetrylowering crystallographic phase transition near 25 K, and adopts an orthorhombic structure (Pmmn) below this temperature. This structural distortion is unlike those observed in the analogous Fe compounds. Magnetic phase transitions are observed in both compounds which suggest antiferromagnetic ordering of lanthanide moments occurs near 7.0 K in TbRuAsO and 10.5 K in DyRuAsO. The nature of the structural distortion as well as thermal conductivity and heat capacity behaviors indicate strong coupling between the magnetism and the lattice. The behaviors of both materials show magnetic ordering of small moments on Ru may occur at low temperatures.