Who designed these chairs?  

Look at the link on the right side under Buy and Sell on this page.  Room of Art is selling 6 DR chairs that look like yours.  

I had asked about these same chairs a while back:
http://www.designaddict.com/forum/General-discussion/Mogens-Kold
They are very similar to the Moller 71, but are actually more sculptural and organic, with a lot of rounded edges.  Very similar, but not the same, as you noted.  I do not know that anyone has said anything definitive about who made them.
Hovmand Olsen designed the 71 chair for Moller, but also did chairs for Mogens Kold.  These chairs remind me of Mogens Kold's way of doing things -- the shape of the front rail of the chair seat, the wide, straight side rails of the chair.  I have wondered if your chairs were a design Hovmand Olsen did for Mogens Kold.  Howard Moon had also shown Rastad and Relling to be a possibility, as they also have a lot of similarities. 

What tchp said.  I don't think anybody knows, yet.  
The underside of the chairs might be illuminating.  Unfortunately they are upholstered, not danish cord, which would be even more illuminating.  Especially with Danish cord, different companies/designers did things differently, and it can be very revealing.

I think your best chance of finding more of these chairs is to just continue looking for Moller 71 chairs, since these are going to be routinely mistaken for them.  Yours appear to have been often made of rosewood (or a wood that is likely to be identified as being rosewood), so searching online for "rosewood Moller 71 chairs" might eventually turn up something.

The seat rails are very reminiscent of Mogens Kold. You will see the same shapes on the Hovmand Olsen for Mogens Kold. Unfortunately they didn't mark their product regularly. 

Thank you all for the reactions. I did see the discussion tchp mentioned, but I was not able to figure out an answer, because these are different chairs. I thought that discussion was about the designer of those chairs. Sorry, I hope it does make sense, my English is not great. I will also start looking for Hovmand Olsen and Mogens Kold, hopefully it will speed up the result. It's irritating that there are no marks on the chairs, like Leif said.
greetings from Ruud

The chairs tchp posted about sure look like the same model chairs to me. How do they differ?
And I would not focus too tightly on Mogens Kold.  Your chairs could be by just about anybody. I have seen lots of chairs that look a lot like the Møller 71 in one way or another and mostly nobody knows what they are. 

Thanks for the replies, I will start looking for the different designers and fabrics, hopefully I can find them that way.
greetings from Ruud