sharepoint server – Sime Users does not see any search results but the access are correctly set

I have the following scenario:

Some One Sitelib, that contains news. These Sites will created / modified and finally published.

Now on the startpage I created a search result webpart to diplay the news (wir custom query on the contenttype).

Now the problem.

Some users will get the Sites in their search results.

But some other users not.

I thought that the access rights are wrong, but they have all the same access to the sites.

Because (all) users can access the sitelibs and can also display the newspages itself.

We did not use any custom security trimmings or s.th.

If there any suggestion where I can look, or how I can check the correct access rights from the search result?