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This article proposes an extension to the Engle-Granger testing strategy by permitting asymmetry in the adjustment toward equilibrium in two different ways. We demonstrate that our test has good power and size properties over the Engle-Granger test when there are asymmetric departures from equilibrium. We consider an application--namely, whether there exists cointegration among interest rates for instruments with different maturities. This issue has been widely tested with mixed results. We argue that either cautious policy, or possibly opportunistic behavior on the part of the Federal Reserve implies that an equilibrium relationship between short- and long-term interest rates exists but that adjustments from disequilibrium are asymmetric in nature. Empirical tests using U.S. yields confirm the asymmetric nature of error correction among interest rates of different maturities.