The Liberty Stadium will welcome Cardiff City for the first time
Police said they were ready to deal with any trouble as Cardiff City fans travelled to Swansea for the clubs' first major meeting in nine years.
Supporters' trusts at both clubs also called for fans to make the match a memorable one for the right reasons.
Phil Sumbler of the Swansea trust said the game should show "the raw passion and sporting rivalry that exists in south Wales in its true light".
The Carling Cup match at the Liberty Stadium kicked-off at 1945 BST.
Police said they would put in "appropriate measures" to deal with any trouble "efficiently and effectively".
I truly believe that fans have matured over the last decade or more and hope the event passes without any serious incident
Assistant Chief Constable Robert Evans, South Wales Police
Assistant Chief Constable Robert Evans said: "Our aim is to ensure the vast majority of law-abiding fans enjoy the day for what it is - an eagerly awaited and much celebrated fixture that should be remembered for what happens on the pitch, and not off it.
"It is extremely important that people of all ages can enjoy and savour the atmosphere in and around Swansea without feeling intimidated by small sets of mindless people intent on bringing the game and the area into disrepute," he added.
"There is clearly much history between both Cardiff and Swansea, and I am in no doubt that sceptics may feel that trouble is inevitable.
"It is South Wales Police's job to prepare for any eventuality, and we have done that, but I truly believe that fans have matured over the last decade or more and hope the event passes without any serious incident," he said.
Violence at a Cardiff-Swansea match at Ninian Park in 1993 led to fans being banned from attending matches.
But Mr Sumbler said football had moved on from problems of violence in the past and was now attracting a more family-orientated generation of fans.
"Let us all contribute to making this game a true Welsh sporting experience that will attract increasing numbers to support our football clubs," he said.
The acting chairman of the Cardiff City Trust Paul Corkrey said: "We are all aware of the emotion and intensity that surrounds this traditional derby match, and without that fervour the game would inevitably be a lot poorer.
"However, it is the responsibility of us all, as supporters of each club, to ensure that such passion does not extend beyond the boundaries of acceptable behaviour."
DIVISION
Police warned motorists of heavy traffic at the Liberty Stadium and in Morriston, Landore and Llansamlet and advised drivers to avoid the areas or to leave extra time for their journeys.
Cardiff and Swansea last played each other in the FAW Premier Cup in 2002, but this year will be the first time they have played in the same division of the football league since 1999.
Coverage of the match was available on the BBC Sport website and on BBC Radio Wales FM in the south-east and south-west.
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