Hello!
If an American citizen (guy) wants to marry non america citizen (gal) what is the legal age of documentation procedure for the non america (gal)? She should be 18 at least?

The legal age in the USA is 18 in each state, as far as I'm aware.

Minors are allowed to marry with their parent's consent; I believe the minor's age for this to be allowed varies by state. Which state are you asking about?

Can I ask why the rush to marry?

Oh, shoot. I somehow missed that the girl isn't an American citizen. (I've asked that the thread be moved to Immigration Law)

She needs to obtain citizenship first before any marriage can be legal. If her parents are not citizens, then I believe she WILL need to be 18 before she can marry.

Both parties must be at least 18 y/o, but on immigration issue, the US citizen must file tax return for 3 years before he/she is eligible to sponsor foreign spouse... so it's recommended to marry and file papers when you are 21.