Out-of-State Marriage: If I Marry Out of the U.S. a, is It Valid Here in the USA

My question involves marriage law for the state of: Arizona.

I'm planning on marrying a girl in another country (Guyana) and going to live over there. (This is a real marriage, and we both love each other). We have decided we will stay over there.

Given we ever split up, will my marriage be valid in the US? Will I have to go through the divorce process in the US or only in Guyana? If we divorced, would I have to pay alimony from the US to Guyana?

Out-of-State Marriage: If I Marry Out of the U.S. a, is It Valid Here in the USA