Some Creationists think there were no death before the fall. But this is contradictory to Scripture.
The reason why some people think there were no death before the fall is that God called His creation "very good". Death is assumed to be somehow bad, so they think there was no death in a "very good" creation.
However, Scripture clearly tells us about the world of creation, and that was a world containing death. Otherwise, what about all the bacteria that live in our bodies? What would happen if Adam steps on an ant? What if a squirrel falls from a tree? Is the death of bacteria, insects, squirrels no "real death", and if so where is the boundary?
In a world without death there can't be any animals and nothing else that could cause accidental death, such as rivers, trees, mountains and so on. There you see that the "no death" idea is obviously in contradiction to Scripture that describes Eden as a world just like ours, and Adam not as an immortal superman but as a human like us.