I'm an Australian Citizen with a US Permanent Residency Green Card & I want to marry my Mexican citizen fiance?

If you marry here you will have all kinds of headaches it's best to file for a fiance visa I-751 I believe and once you get it marry him and bring him here You say mexican citizen is he in the U.S. on a green card or work visa? if not he could be deported and you would have to go threw all kinds of red tape to keep him here. Best to find out the requirements for the I751 at www.uscis.gov click on I AM a and choose a selection then choose what you want to do and it will tell you the forms and the cost for filling the forms out. hope this helps and the process once started can take up to 5 or 6 years to complete.