“See you later, alligator” is a catchphrase, an expression meaning “goodbye.” The words are taken from a popular rock-and-roll song of the fifties. It was written by a Cajun from my area of Louisiana and made famous by the group, Bill Haley & His Comets. The song refers to what the singer’s girlfriend says to him when she leaves him for another man. But, when the girlfriend changes her mind and wants to return to the singer, it is also what he says to her.
The expression became very popular with my generation and is more like “see you later” than “goodbye.” It was often shortened to “later gator” and the response was “in a while crocodile.”
Among the young GIs who had been stationed in Germany, it became “später gator.”