It is not known as a "big rivalry" as such, but both of these clubs certainly have a dislike for one another. The main reason for this is around the mid 80's and through to the near past both clubs have been in the same divisions and have had relegation and promotion battles with eachother. As well as that they are reasonably local to each other to.
Crystal Palace fans have mixed views on who their main rivals are. Some say Brighton are, others argue that it is Millwall or QPR.
The Majority of Brighton and Hove Albion fans would class Palace as their main rivals but there are some that have more dislike for Portsmouth.
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