I joined the armature for eye animation with the armature for the head animation by Ctrl+J. Right after that the head becomes very small rotates 90 degrees and jumps into one of the eyes.
If I hide the head mesh, then the eyes become very big, move above head and overlap.
I managed to partially solve the problem by unparenting meshes from the armatures, then joining the armatures by ctrl+j and then parenting back the eyes. It all worked OK, but I cant parent back the head, as it get deformed in a very strange way.