Complexation of $Cd^{2+},;Pb^{2+};and;Hg^{2+}$ ions with four cryptands were studied by potentiometry and solution calorimetry in various weight percent methanol-aqueous solvent at 25${circ}$C under $CO_2$free nitrogen atmosphere. The stabilities of the complexes were dependent on the cavity size of macrocycles. The $Hg^{2+}$ ion stability constants are higher than those of $Cd^{2+};and;Pb^{2+}$ ion. All the cryptands formed complexes having 1 : 1 (metal to ligand) mole-ratio except for $Hg^{2+}-L_1$ (cryptand 1,2b: 3,5-benzo-9,14,17-trioxa-1,7-diazabicyclo-(8,5,5) heptadecane) and $Cd^{2+}-L_2$ (cryptand 2,2b: 3,5-benzo-10,13,18,21-tetraoxa-1,7-diazabicyclo (8,5,5) eicosane) complexes. $Hg^{2+}-L_1$ complex was a sandwitch type, and the $Cd^{2+}-L_2$ complex showed two stepwise reactions. Thermodynamic parameters of the $Cd^{2+}-L_2$ complex were $6.08(log;K_1)$, -7.28 Kcal/mol $({Delta}H_1)$, and $4.78;(log;K_2)$, -4.62 Kcal/mol $({Delta}H_2)$, respectively, for 1 : 1 and 2: 1 mole-ratio. The sequences of the selectivity were increased in the order of $Hg^{2+};>Pb^{2+};>Cd^{2+}$ ion for $L_3;and;L_4$ macrocycles, and the $L_2$-macrocycle has a selectivity for $Cd^{2+}$ ion relative to $Zn^{2+},;Ni^{2+},;Pb^{2+};and;Hg^{2+}$ ions. Thus, it is expected that the $L_2$ can be used as carrier for seperation of the post transition metals by macrocycles-mediated liquid membrane because $L_2$ is not soluble in water, and the difference of stability constants of the metal complexes with $L_2$ are large as compared with the other transition metal complexes. The $^1H;and;^{13}C-NMR studies indicated that the nitrogen atoms of cryptands have greater affinity to the post transition metal ions than the oxygen atoms, and that the planarities of the macrocycles were lost by complexation with the metal ions because of the perturbation of ring current of benzene molecule attached to macrocycles and counter-anions.