We explicitly construct infinite families of the maximal real subfields of cyclotomic function fields over the rational function field k=F_q(T) whose ideal class groups have arbitrary l^n-rank for n = 1, 2, and 3, where l is a prime divisor of q-1. We also obtain a tower of cyclotomic function fields K_i whose maximal real subfields have ideal class groups of l^n-ranks getting increased as the number of the finite places of k which are ramified in K_i get increased for a positive integer i. This is a joint work with Yoonjin Lee (Ewha Womans University).