A random variable X is said to be self-decomposable (benceforth, SD) if it satisfies tbe fol- lowing eguivalence relation in distribution X = (a*X') o (Xa) for alı positive a in some öpen interval. The operation * is either multiplication or addition and tbe distribution of the co-random variable Xa depends on tbe constant In this paper we study SD random variables where the operation o defined to be maximunî. Some properties of such random variables are given and a representation theorem is stated for discrete and continuous random variables for the univariate case.