Many people believe they've seen pumas, leopards and panthers across the country and some claim to have been attacked by them.
Occasionally they've been photographed or even shot and caught.
Lena the lynx
In May this year a lynx was found in a North London garden. Lena's now in London Zoo but it's not known where she came from.
It's thought lots of big cats were released into the wild when it became illegal to own one without a £3,000 licence in 1976.
And experts from the BCCS think they could've started breeding with each other which could explain why in 2000 alone there were more than 250 reported sightings!
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