This paper examines the stability of import and export demand functions for the United States over the 1975q1-2001q2 period. Using the Johansen maximum likelihood approach, an export demand function is readily identified. In contrast, there appears to be a structural break in the import demand function in 1995; specifications incorporating this break pass tests for cointegration, although the price elasticity is not statistically significant. Only when excluding computers and parts from the import series is a stable import demand function detected. The resulting point estimates confirm the persistence of the income asymmetry first noted by Houthakker and Magee (1969), although in a slightly diminished form. One policy implication of these findings is that dollar depreciation --unaccompanied by a realignment of growth trends --is insufficient to substantially reduce the US trade deficit.