A theoretical equation of the reversible current -potential curves is derived for the competitive ion-transfer of two kinds of cations present in an aqueous (w) phase simultaneously facilitated by a macrocyclic ligand (L) present in an organic (o) phase. Especially, for the two limiting cases, i.e. case (A): c(M)*(i) (j = 1, 2) much greater than c(L)* and case (B): c(L)* much greater than c(M)*, (where c(M)*(j) and c(L)* denote the bulk concentrations of cation Mi in the w-phase and of L in the o-phase, respectively), simple explicit expressions are derived and a method analyzing the facilitated waves is presented. Furthermore, the main part of the theoretical predictions obtained is verified experimentally at 25 degreesC by using the ion-transfer-polarographic method with the electrolyte dropping electrode, for the following four combinations: (i) competitive cations: protonated alanine and H+. L: benzo-18-crown-6 ether; (ii) Na+ and Li+, benzo-15-crown-5 ethers (iii) K+ and Na+, dibenzo-18-crown-6 ether, and (iv) Na+ and Ba2+, dibenzo-24-crown-8 ether.