Alligators actually don't breathe underwater. Though they can stay submerged for long periods of time, they must eventually surface to breathe through the nostrils on their long snouts.
Among the many successful adaptations that have allowed alligators to remain largely unchanged over thousands of years is the ability to stay submerged for more than an hour at a time. This ability is aided by the alligator's heart, which slows down when the animal submerges, allowing the body to use oxygen more efficiently. Not breathing in water is essential to the alligator's survival. In fact, this large reptile has adapted nose flaps that clamp shut and block water from entering when the gator dives underwater.