Pure, fully textured and c-axis oriented Sr2FeMoO6, films were deposited on SrTiO3 and (LaAlO3)(0.3)(Sr2AlTaO6)(0.7) substrates with different thicknesses. A decrease in substrate induced strain was observed in films on SrTiO3 with increasing thickness, but the strain in the films on (LaAlO3)(0.3)(Sr2AlTaO6)(0.7) was nearly constant within the whole film thickness range. Despite the differences in the strain, the magnetic properties of the films showed similar thickness dependence on both substrates. The saturation magnetization and Curie temperature increased until around 150 nm thickness was reached. Semiconducting low temperature upturn in resistivity was observed in all the films and it was enhanced in the thinnest films. Thus, the band gap energy increases with increasing film thickness. According to these results, at least 150 nm thickness is required for high quality Sr2FeMoO6 films.