Axis deer hunting is a pretty big business here in Tx. To my knowledge they are not considered a nuisance. They are great eating, beautiful animals and in some areas are plentiful. There are some other exotic species that are considered a nuisance to some, Aoudad, and Sika deer come to mind. Also, even though feral hogs are great problem here, they have become big business as well. It is unfortunate, but in Texas the majority of the state is privately owned land. Ranchers have learned that they can make alot more money game ranching and hunting than they can strictly running cattle and growing taters. I wish I could help you out, but if you want to hunt Axis in Texas, atleast nice ones, then it will cost a pretty penny.
Here is an example of how feral hog ranching/hunting has become big business.
www.texaswildhoghunting.comThey buy trapped feral hogs, casterate them, release them into 20 acre enclosures after they get fat and semi tame and hunters from all over the country come and pay to shoot them. My sisters 26 acres is a couple hundred yards from this ranch. Very nice people to be sure, but you can hear the shots being fired all day long...