Nevermind…
… just when I wanted to give up, I found the error and could help myself to solve this:
I used on top of my custom CSS the:
a:hover{}
And further down, within the CSS for responsive cases (@media only screen)
– nav .menu li a {}
– nav .menu li a:hover {}
– nav .menu ul li.current-menu-ancestor > a, nav .menu ul li.current-menu-item > a {}
Sorry for bothering you and I wanted to let you know that I solved it, so that you don’t need to spent time on this issue.