We present an experimental study on the epitaxy and orientational relationships of WO2 and NbO2 films on (0001) Al2O3, (111) MgAl2O4, and (111) MgO substrates, as well as WO2 on (111) SrTiO3. The higher symmetry of the substrate planes compared to the film planes leads to the formation of epitaxial structural variants, and they are related by the surface rotational symmetry elements of the substrates. WO2 and NbO2 crystallize in distorted versions of the rutile structure, and we discuss our findings in context of the rutile unit cell. Our results are applicable to other compounds that occur in (distorted) rutile structures. For the case of NbO2 thin films, we also demonstrate that they can be grown epitaxially on (10
2) and (10
0) Al2O3, lower symmetry surfaces; in these cases, surface symmetry does not induce the formation of epitaxial rotational variants, though domains related by glide symmetry are possible.