@VinDSL,
Thank you for your reaction! I see that your swappiness is set to 10.
@AndyInMokum,
Thanks for replying! According to your advice I dropped my swappiness to 1, and till now I didn't have any problems with that. I notice that my memory level is higher than before, but that's just the goal of it: to put more in memory in stead of swapping to the HDD all the time! 
I continue to work with this 1-level and if there are remarkable things that show up, I will let know here.
As I wrote I would let know if something showed up, well, it did.
As I updated Thunderbird, and put some add-ons to it, it really stuck and the whole system became so unresponsive that I had to wait several minutes to become responsive again, only by closing every running program. My CPU monitor was on 100% all the time.
I know the cause was Thunderbird, but this kind of absence of a working machine had much to do with the swappiness of 1. So I changed it to 5, and now I just experiment with this amount, in order to see if this is a better number in my situation.
Till now it is just fine, so I guess swappiness of 5 is a good compromise and literately the (rounded) average of 1 and 10.

paulus