Wolverine: Bulldog 

Storm: Cat

Cyclops: Brown Labrador

Professor Xavier: Chimpanzee

Jean Grey: Red Fox

Emma Frost: Raccoon

Psylocke: Weasel

Rogue: Skunk

Colossus: Gorilla

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Please note: some of these draw direct inspiration from the (now deceased) X-animals of the Mojoverse in X-men comics