One of the premises of my old west game is that the people who immigrated to America have been followed by the creatures that roam their native land. how would this "Invasion" of America by these foreign entities be regarded by the spirits native to the land? For instance: How would a Thunderbird react to a Griffin in it's domain? With aggression? With caution? Or, would the Thunderbird simply ignore the Griffin? 

  Any thoughts?

Of course there would be conflict; otherwise it would be boring.

Are we talking spirits, physical beasties or spirits that can manifest as physical beasties?

Are the native spirits associated with a player characters as familliars, guardian spirits, or somethign like that? If so, you could have some interesting interactions other than conflict. Some entities might hit it off, which could take things in a very different direction.

An alien predator, like a griffin, would probably decimate buffalo and horse herds. They wouldn't be popular. There would be bounties. Saying that, a griffin feather headdress might be a highly sought after possession. What would it mean for a native shaman to take a creature like a griffin as his totem animal?

Bert

  Physical creatures and spirits both tangible and intangible, with some intangible spirits able to take physical form.

  The Shaman has a spirit of a native animal (Cougar,etc.) as his totem animal and can call upon aspects of his Totem for aid. As far as a Shaman having a Totem not native to North America, I had not considered that as a possibility. I like it.