For example, are you asking about:
* Predators and prey? Like a lion and a zebra, or a hawk and a mouse?
* Animals that compete for resources? Like a wolf pack and a coyote pack, or a group of birds fighting over a nesting site?
* Animals that cooperate? Like a meerkat colony or a herd of elephants?
* Animals that are neutral towards each other? Like a deer and a squirrel, or a cat and a dog?
Once I know what animals you're referring to, I can tell you how they might react when they come near each other.