Value and momentum strategies both have demonstrated power to predict the cross-section of stock returns, but are these strategies related? Measures of momentum and value are negatively correlated across stocks, yet each is positively related to the cross-section of average stock returns. We examine whether the marginal power of value or momentum differs depending upon the level of the other variable. Value strategies work, in general, but are strongest among low-momentum (loser) stocks and weakest among high-momentum (winner) stocks. The momentum strategy works, in general, but is particularly strong among low-value (expensive) stocks. These results hold despite finding comparable spreads in value measures among stocks with different levels of momentum and comparable spreads in the momentum measure among stocks with different levels of value. Any explanation for why value and momentum work must explain this interaction.