The quality of epitaxial film significantly depends on the substrate material. The oxide superconducting film growth is also the case. In the present work, Ln₁Ba₂Cu₃O_y (Ln=Y, Nd, Er) films were grown by the reactive rf-magnetron sputtering on (100), (110)-SrTiO₃ and (100)-MgO single crystal substrates. To get more information on the growth mechanism, the initial growth stage (growth thickness of 1-3nm) was closely studied. MgO served as an excellent substrate on which even two monolayers of YBaCuO grew epitaxially with very smooth surface. The films grown on both (100) and (110)-SrTiO₃ required thickness more than 10nm to obtain epitaxial-like RHEED pattern. The RHEED pattern itself still looked spotty, showing the surface roughness existing even for 100nm thick film grown on the SrTiO₃ substrate. The heteroepitaxial and double-heter-oepitaxial (superconbuctor/insulator/superconductor) technologies are also demonstrated in the text.