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1.
A method of urinating in public waters involving floating motionless face down in the pool, lake, etc. as the deed is done, similar to an alligator in wait.
Is Jim okay? Yeah, he's just taking care of business gatorstyle.
by Shadowpossum July 13, 2011
 
2.
The sexual act of being done anally on the back of a gator.
1. Josh and Dan did gator style all night long.

2. Daniel: "DO ME FROM BEHIND ON A GATOR"
by BLee1 August 23, 2009