Alligator is signed by taking both open hands and chomping them together - opening and closing like the jaws of an alligator. For added effect, extend both arms as if they're the long jaws, and curve your fingers so they look like sharp alligator teeth, before you chomp them together.
As with all the animal signs, adding some sound effects and a bit of vaudeville acting help make the signs more fun and more memorable for your baby.
Alligator and the other animal signs are great fun for most babies. Take advantage of their natural curiosity about animals and teach the sign and the associated sounds for each animal. For an animal like alligator (which you hopefully don't have lurking around your house), you can teach the animal sign in conjunction with alligator toys, flash cards, or videos, or when you visit the zoo.
Introduce your baby to alligator and other exotic animals by reading picture books or by visiting the zoo. We also enjoy using toy models to familiarize our babies with animals not commonly found in farms or households.