The fluttering of the foreleg claws seen in red eared sliders is often a courtship behavior exhibited by males. The male will often swim backwards in front of a female, "tickling" her cheeks, and will do this fluttering to entice the female prior to mating. However, it is not limited to males in courtship -- both females and males will exhibit this behavior at other times as well and it is thought to communicate dominance or territoriality. The turtles in this video are both males and are both exhibiting the behavior, so this is most likely a dominance or territory issue rather than courtship!
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