Hi Marius,
that was the solution!
The definiton "overflow: hidden" was not defined in styles.css.
I did not create the WP Site, it was done by a grafic-designer. I have been asked by my customer, as he could not get hold of the grafic-desgner of the Site anymore, if I could solve the problem,
I put the css declaration within the custom css and now it works for the Browsers IE 11 upto 9! as well. Cross browser tests on Firefox worked OK too up to verison 30, older ones I did not check.
Thank you very much for your good advice/help.
Have a nice weekend,
Angel Luis