  We introduce the concept of associativity for string functions, where a
string function is a unary operation on the set of strings over a given
alphabet. We discuss this new property and describe certain classes of
associative string functions. We also characterize the recently introduced
preassociative functions as compositions of associative string functions with
injective unary maps. Finally, we provide descriptions of the classes of
associative and preassociative functions which depend only on the length of the
input.
