Table & chairs I'd  

start with....
Steen Østergaard and see where you end up.

thanks Killian! Glad to see...
thanks Killian! Glad to see you're still around!

The chairsf look to be by Alexander...
The chairs look to be by Alexander Begge for Casala

how to clean?
any idea how best to clean them? the abs (or whatever kind of plastic they are) has yellowed and gone dull. I don't want them to be bright shiny new, but just to get rid of stains & have wee bit of sheen would be nice. My mother is threatening to paint them for me but I'm not fond of that idea at all. Dad says I should bring them home and let him take the auto buffer to an inconspicuous place and see what happens.

try a magic eraser
it will take the dirt off but I doubt it will get rid of the yellowing of the plastic. Try it out on the undersurface of the chair.

Yellowing...
I'm not sure if these would work but it might be worth a shot...
http://retr0bright.wikispaces.com/

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While I have not tried retrobright, I can certainly attest to the efficacy of using hydrogen peroxide...
I had some yellowed plastic parts from some vintage Braun things and submerged them in Hydrogen Peroxide for a few days. It worked like a charm.
While I realize soaking the chairs in that much HP is ridiculous, perhaps the retrobright product or something comparable containing HP might actually work.
I wouldn't use any kind of magic eraser on plastic of any kind, it will scratch...

solange
it has caused scratching when you used it on plastic or are you just hypothesizing?

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in my experience jdip yes... very, very fine scratches that dulled the plastic shine.
Perhaps a result of applying too much pressure, or perhaps not best suited for shiny plastic...either way...it did change the finish and I was not happy with the result.

thanks for the heads up
I had only tried them out on my parents ugly white plastic outdoor patio furniture and they did wonders. I did note that if the plastic has a sheen to it it will be dulled but I assume the posters chairs lack that sheen.

Magic eraser
It has always been my experience that magic eraser works best with extremely little pressure and lots of water. Anything anyone would call scrubbing has not worked nearly as well.
And I would have a hard time imagining that would cause scratches, for whatever it is worth....