It seems that the actual versions of xampp are for 32bit-versions of Windows operating systems. But after some search in the internet I found the good hint that all the parts of the xampp package are also alone available and I just needed the webserver (apache), php and mysql and all three are available in a 64 bit version.
I've downloaded that three that are normally part of the package, installed them make some changes in the configuration (I found a tutorial on the internet for this) and it worked.