We look for evidence of "hysteresis" in the U.S. unemployment rate - that is, that current labor market outcomes affect the future equilibrium level of the unemployment rate. We first examine (using a variety of econometric tests for unit roots) whether the unemployment rate tends to come back to a long-run average over time. On balance, our results suggest that the unemployment rate tends to return to a long-run value, ruling out the possibility of permanent hysteresis. We look for evidence of temporary hysteresis by examining whether lagged unemployment enters a standard Phillips-curve model of U.S. inflation. We find week evidence in support of temporary hysteresis, but the effect is not large, suggesting that hysteresis is not very important for U.S. unemployment.