A general spectroscopic method is described for studies on the complex formation between metal ions and ligands, and is applied to $Cu^{2+}$ and $Ca^{2+}$binding to glycosaminoglycans. The order of binding constants for both ions is heparin >dermatan sulfate >chondroitin sulfate. The electrostatic forces are shown to be the predominant factor in the interaction. The 2- to 3-fold higher affinity for $Cu^{2+}$ than for $Ca^{2+}$ is obtained for heparin and dermatan sulfate, but little difference for chondroitin sulfate. These results are explained as chelation of both carboxyl and sulfate groups to $Cu^{2+}$ in former cases. The difference of binding constants among glycosaminoglycans is related to proposed various biological functions of the biopolymers.