Many recent studies have focused on the relationship between American Depository Receipts (ADRs) and their foreign underlying stocks, because of the price interaction and arbitrage opportunities provided by the dual listings. The cointegration and its corresponding error correction model employed in some recent studies assume that the tendency to move towards a long-run equilibrium is present all the time. However, the presence of costs of adjustments may prevent economic agents from adjusting continuously. As an extension of previous studies, this paper applies the threshold cointegration model that allows for asymmetric adjustment towards a long-run equilibrium to inspect the linkage between Taiwanese ADRs and their underlying shares. By employing the threshold error correction model, the short-term adjustments also are examined. We find some evidence of asymmetric adjustments in our data. The tests for asymmetries are also implemented with the maximum likelihood estimation for the complete multivariate threshold cointegration model instead of the univariate model.