The microstructure of several YBa2Cu3O7-x superconducting thin films has been investigated by transmission electron microscopy. Films, with a thickness ranging from 250 to 500 nm, were grown by triode sputtering on (001) SrTiO3. The films are amorphous upon deposition. After annealing in oxygen, epitaxial grains are found. Depending on the annealing conditions, a high density of twin boundaries was observed. X-ray diffraction shows that the orientation of the majority of the grains changes with film thickness. In the thinner films (250 nm) the c axis is preferentially oriented perpendicular to the substrate. In thicker films a preferential a orientation is observed. High-resolution electron microscopy (HREM) reveals that both types of films show an initial growth with the c axis perpendicular to the substrate. Films with a thickness in excess of 500 nm also showed the presence of randomly oriented grains with no orientational relationship to the substrate. It is concluded that the nucleation process at the substrate-film interface is not determined by the lattice match, but rather by the favorable interaction of one kind of the YBa2Cu3O7-x metal-oxide layers with the substrate surface.