In the United States and Latin America, candidates for national and state-level office frequently must win primary elections in order to advance to the general election. We model policy and valence issues for office-seeking candidates facing such two-stage elections. We determine a Nash equilibrium for the candidates' optimal strategies, and we find that holding a primary is likely to increase a party's chances of winning the general election, particularly in situations where valence issues that involve the candidates' campaigning skills and that are not known prior to the campaign are more salient than policy issues. Furthermore, we find that primary elections are especially likely to benefit parties that expect to be underdogs in the general election. Our conclusions are directly relevant to U.S. politics and by extension to the strategic decisions that many Latin American parties currently confront, about whether it is strategically desirable to hold primaries.