Orientation relationships (ORs), interface planes and growth directions of the directionally solidified eutectics NiO–YSZ, CoO–YSZ, NiO–CeO2, NiO–GDC, CoO–CeO2 and CoO–GDC have been determined by means of electron backscatter diffraction (EBSD). The eutectics were prepared by the laser floating zone technique at different growth rates (10–200 mm/h) to explore dissimilar lamellar spacing. The majority OR is characterized by a single (1 1 1)NiO/CoO//(0 0 1)YSZ/GDC/CeO2(1 1 1)NiO/CoO//(0 0 1)YSZ/GDC/CeO2 interface plane and two different growth directions: [0 1¯ 1]NiO/CoO//[0 1 0]YSZ/GDC/CeO2 and [1 1 ¯0]NiO/CoO∼//[1 1 0]YSZ/GDC/CeO2, the OR being the same for both cases. In addition, a cube-on-cube OR, where the crystallographic axes of the component phases are parallel, has also been observed. These experimental results are discussed in terms of the ionic charge balance and the lattice misfit at the interface. The coincidence of reciprocal lattice points model (CRLP) has also been applied to the NiO–YSZ case. The most favourable ORs predicted by the CRLP model are consistent with the experimental findings.