Thin-films of yttria-stabilized zirconia (YSZ) and Y2O3 (cubic structure) have been grown on annealed substrates of (0001) and {10 (1) over bar 0} Al2O3 (alpha-Al2O3, corundum structure) by pulsed-laser deposition. These model systems demonstrate the effect that surface structure, such as surface steps and facets, can have on ceramic thin-film growth. The near-(0001) Al2O3 surface facets into a terrace-and-step morphology where the terraces correspond to the (0001) surface. YSZ grew on, or near, surface steps on the nominally (0001) surface such that it was preferentially aligned with the (110) YSZ plane parallel to the (11 (2) over bar 0) Al2O3 plane. On the large (0001) terraces, the grains grew so that the (110) YSZ plane was aligned parallel to the (10 (1) over bar 0) Al2O3 plane. The {10 (1) over bar 0} Al2O3 surface facets into a hill-and-valley structure that corresponds to the {10 (1) over bar 2} and [10 (1) over bar (1) over bar} planes. Growth of Y2O3 onto this surface again produced two different orientations. For growth which occurred on the {10 (1) over bar (1) over bar} facet, grains of Y2O3 where aligned with the (111) Y2O3 plane parallel to the (0001) Al2O3 plane, while for the growth on the {10 (1) over bar 2} facet the (001) Y2O3 plane was parallel to the (1 (2) over bar 10) Al2O3 plane.