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27 August 2015 Last updated at 17:56 BST
Both games are free to play but have some features which cost money to add.
The Advertising Standards Agency, the UK authority in charge of checking advertising, say that the games put too much pressure on children to buy these additional features.
That's because they say things like 'Moshi Monster needs you', or tells players they will be 'super popular' if they pay to become members.
Now the companies behind both Moshi and Bin Weevils say they have changed the games and will stick to the rules in the future.
Watch Newsround reporter Jenny's full report on this.
The popular online games Moshi Monsters and Bin Weevils have found themselves in trouble for putting unfair pressure on children to make in-game purchases.