BOTH Port Adelaide and Adelaide are facing allegations that fans racially abused opposition indigenous players during Saturday night's Showdown at the Adelaide Oval.

The Power is investigating allegations that one of its supporters racially vilified Crow Eddie Betts, while there are also claims involving alleged racial abuse of Power ruckman Paddy Ryder by a Crows fan.

On Monday night, the Power said they were investigating the matter with stadium management, adding they would not tolerate such behaviour from their fans. 

"If a club member has been found to breach Port Adelaide's spectator code of conduct the offender's membership can be revoked indefinitely," the club said in a statement.

Meanwhile, the Power are also looking into claims that Ryder was a target of racial abuse from a Crows supporter during the same match. 

The club said it would not comment further until both investigations were completed.

In a statement on Tuesday morning on the Betts allegations, Adelaide CEO Andrew Fagan said, "Our club strongly condemns any such behaviour and finds it abhorrent and disgusting.

"In listening to our playing group and our Aboriginal and Torres Strait Islander players in particular, it is clear how damaging and impactful racism is to them and their families.

"Our entire playing group and our club stand together on this, unequivocally."

A Crows spokesman told AFL.com.au on Tuesday that the club would not comment on the allegation concerning Ryder until it was confirmed by Adelaide Oval officials.

The AFL said in a statement on Tuesday it was working with SA Police in its investigations.

CEO Gillon McLachlan commended both clubs on their public statements, and said that the football community must continue to be vigilant and call out racism whenever it occurs. 

"Racism is hurtful and damaging to individuals and communities, and when it happens in football, we must call it out," he said. 

"Our game has a responsibility to our players, and a role to play in the community on issues of racism and vilification. Our players deserve respect, and we ask that people understand the impact of their comments on them, their families and our community.

"We know our game can do more, and I will continue to work with our General Manager Social Policy and Inclusion, Tanya Hosch, on continuing to evolve our match day policy, and explore opportunities to educate our communities."

AFL Players' Indigenous Advisory Board chair Shaun Burgoyne said in a statement, "We're sad that our brothers and sisters are still experiencing racial vilification despite the ongoing education and promotion done within the football industry and wider society.

"This has been happening for far too long and we, as indigenous footballers, have had enough. We deserve more respect than we are being shown.

"The abuse directed towards players is more than just words and people need to understand the impact that it has on the player, their family, their children and their community.

"While it's heartening that these incidents are being called out, there's a lot of work to do before we can claim to be a truly inclusive game."

AFL Players' Association CEO Paul Marsh said, "No AFL footballer, and no person for that matter, should have to experience any form of vilification in their workplace.". 

This is not the first time the Showdown has attracted antisocial, racist behaviour. 

In round 22 last year, a female Port Adelaide member was banned indefinitely after being filmed throwing a banana towards Betts in a racially motivated attack.