Despite their potential application in strain-engineered layer structures, the epitaxial growth of rare earth scandate films on cubic perovskite substrates is not fully understood to date. Here we report on the epitaxy of the orthorhombic GdScO3 and DyScO3 on (001) BaTiO3 and SrTiO3 thin films. In particular, the orientation relationship between the orthorhombic epilayer and the cubic substrate is examined by aberration corrected high-resolution transmission electron microscopy. For all cases investigated, the long axis of the orthorhombic unit cell was found to be perpendicular to the growth direction.