The nonlinear wave propagation theory has been applied to predict the breakthrough and regeneration curves of ion-exchange columns for heavy metal removal. Batch experimental tests using IRC-718 cationic resin were conducted to obtain the ion-exchange equilibria of H/Cu and H/Ni systems, and column tests were conducted to obtain the breakthrough and regeneration curves under various operating conditions. The batch experimental results show that the affinity sequence is Cu > H > Ni. The column experimental results show that IRC-718 In H-form is effective for removing copper from synthetic wastewater but not effective for nickel removal. For a copper-rich feed solution, the ion-exchange wave is a self-sharpening wave and its regeneration wave is a nonsharpening one. For a nickel-rich feed solution, the ion-exchange wave is a nonsharpening wave and its regeneration wave is a self-sharpening one. For a copper/nickel mixture feed, nickel gradually appears in the effluent, and a plateau of concentration higher than the feed one is identified. Simple equations based on the nonlinear wave propagation theory have been developed to predict the breakthrough and regeneration curves, and the predicted results are quite comparable with the experimental data.