Hello everybody,
I have the problem that in Category listinging the preview image has the size of 373px (that's good) but is stretched from the XS-image(width 70px). Although the image has been saved in a good quality (width 900px) and is also displayed in a good resolution in the articles. I find no way to improve the quality of the preview image.

imgur.com/o4V3tW8

I'm thankful for every tip

Hello,
At the parameters of K2 at tab Image there is an option Quality (%) used when processing images. Check that the value of this option has a value of 80 or greater.

Thanks Teo,

the quality is 100%. K2 creates all sizes (xs,s,m,l,xl) with a good quality. But in the category listing the xs-file is used and it's streched to 900px.

In the category's settings, you can choose a different image size.
If that category is inheriting its settings from another category then you need to edit the 'master' category's settings.

Hi Krikor,
the size is ok. But the quality is bad. I could change the size and it works. But the template stretches always the small image to the required size. Any idea?

Try a different template for that menu item, any will do for testing.
If the issue is not present, this means that the template has an issue in its overrides. If that is the case, you need to address this issue to the template's developer.