The screws themselves seems no be new

"to be"..... or "not to be"......THAT is the question. 

Couldn't decipher what your actually trying to type.

Anton,
If the nut has no backlash and is rigidly mounted to the table, the coupling has no play,.......... then that leaves the bearing or bearings on either side of the table as the source of backlash. Can you add a little more preload to them?
RICH 

Quote

The screws themselves seems no be new

"to be"..... or "not to be"......THAT is the question. 
Couldn't decipher what your actually trying to type.

Sorry, the screws themselves seems to be new, but a "preloaded" nuts gives this backlash.

Anton, lets start at the beginning here. A ball screw and nut used in a cnc application would 98% of the time be pre loaded. This means [basically] that there is negative clearance in the assembly. This preloads the balls between the nut and the screw shaft to a given value. When a radial or axial force exceeds the preload value, plastic deformation occurs. The result is backlash and a very unhappy ball screw. Otherwise your ball screws should have 0 backlash [to a point!].

If your ball screws have backlash then you have some issues to take up with the supplier [possibly wrong nuts]. Unless as pointed out by Rich, it was a system designed for preloading between two nuts in the first place. 

woolexmail, of course you are right. But you are spoken about ballscrews for big boys.  Because of lack of space in Chinese X2 minimill, Mike (Cncfusion) gets a usual cheap ballscrew with a single nut and "preloads" it by changing balls for bigger ones. Speaking correctly, there are not a true preloaded nuts, but a nuts with minimised backlash.

PS: Today I have downgraded to printer port, so, waiting for backlash compensation implementation in SS plugin.