The clashes in November and April between the two bitter South Wales rivals will be the first ever in the top flight, with the build up to the first meeting at Cardiff City Stadium on November 3 already a red letter day for both sets of fans.
Swans skipper Williams told the South Wales Echo: "It would be nice to win both.
"It's a massive game. I'm not sure what Premier League fans in England think, but for us in Wales it's going to be a massive game.
"The build up starts very early, it's one we are already looking forward to and I'm sure Cardiff are the same. It's a massive day.
"We enjoyed the derbies last time in the Championship and it'll be on a bigger scale now. We'll definitely be looking forward to that and will enjoy it."
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