Which is correct_ " A dog while chasing a cat runs after it or runs behind it. In India many people say ' the dog ran behind the cat' Are both allowed?
'After' is better for me (British English speaker) because it gives the idea of the chase, while 'behind' just describes the position, but doesn't suggest trying to catch it.
I live in the USA and my choice will be "after" too.
I am a NNES.