The crystallographic texture and the grain size have been measured by X-ray diffraction techniques for about 200 nm-thick Cu films sputter-deposited on amorphous Ta35Si18N47 and Ti33Si23N44 underlayers, and for comparison also on TiN underlayers and oxidized silicon, all on Si (100) substrates. The (111) texture of the as-deposited Cu films increases in the sequence TiN < SiO2 < Ti33Si23N44 < Ta35Si18N47 Amorphous Ta35Si18N47 and Ti33Si23N44 layers evidently promote quite effectively the growth of highly (111) textured Cu films. After vacuum annealing at 450 degrees C for 30 min the texture of Cu rises on Ti33Si23N44: falls on Ta35Si18N47, while that on TiN and on SiO2 changes little and the sequence becomes TiN < SiO2 < Ta35Si18N47 < Ti33Si23N44 The grain size of the as-deposited Cu films increases in the sequence Ti33Si23N44 < SiO2 < Ta35Si18N47 < Ti47N53 and rises moderately upon annealing, least for TiN and most for SiO2 and Ti33Si23N44.