I've ran into a Alligators several times when fishing in my kayak (in Texas). I just try to keep my distance and I've been told make sure you don't corner them in a cove or get between them and shore.

FM

I've been fishing around alligators my whole life, and have kayak fished near them for ten years on and off.  More often than not, they dive and hide out on the bottom or resurface farther away from you.  Those that hold their ground or close distance are avoided.  I've also purposely charged alligators in fishing areas to avoid them chasing my frogs or fish, but those are always the smaller variety.  In a decade of being close to the water in a kayak sometimes shorter than they are, I've had one instance of alligator aggression and it was a female making a beeline for my boat because there were babies in the area.  Steer clear of hatchlings and males during mating season.  If you're unsure of your mating season, call the DNR or ask the locals.  I wouldn't trust a gun, I once watched two six footers face off before one went completely airborne from a dead stop.  They're stupidly powerful, fast animals.

Well said. The ones that disappear underwater are the ones that make me nervous. When they are visible at least you know where they are. I have paddled over quite a few in shallow water that were sitting on the bottom. 

5 hours ago, Don51 said:

Well said. The ones that disappear underwater are the ones that make me nervous. When they are visible at least you know where they are. I have paddled over quite a few in shallow water that were sitting on the bottom. 

In my experience, a gator that goes underwater is avoiding you.