I have solved the issue. Turned on "Guess Itemid" at Content Plugin to "Yes".

Meanwhile I have done some extra testing and found the following. For every category there is a menu item. The issue is that the articles per category get the wrong item alias in de SEF URL so I deleted the menu item, trashed it and created it again. Guess what? Now another item alias (still the wrong one) appears in the SEF URL. I repeated this about four times and every time the next item alias is used for the SEF URL.
Menu item rebuild, category rebuild, nothing helps.....

Correction: title of this topic must be "Wrong menu-item in URL".

Please have a look at gordonsbay.travel on the homepage. There are four articles all coming out of the same directory named Gordon's Bay (Alias: gordons-bay).
The first one has a correct path where it has inherited the menu alias from "About us". The other three start with "stay" after the domain name and this is not correct. Those articles come from category Gordon's Bay (Alias: gordons-bay).

You can check this by using menu www.gordonsbay.travel/about and you will see the articles there and not under the menu www.gordonsbay.travel/stay/accommodation.

I used the module articles per category to show these articles on the homepage.
Deleting all SEF URL's an caching has no effect.
Thank!