A substantial literature claims that political parties compete over issues by selectively emphasizing favorable issues and avoiding issues emphasized by their opponents. In recent years, this understanding of issue competition has been challenged by empirical studies showing issue engagement to be the rule rather than the exception. To move the discussion beyond the descriptive question about degree of issue avoidance or issue engagement, this article offers a theoretical framework of issue competition that addresses central but hitherto neglected questions about which parties respond to which parties. The main implications of the theoretical framework are tested in a set of statistical time-series analyses of party interaction in Denmark covering more than 50 years, 24 major issues and 21 elections. These analyses offer support to the ideas that parties are more responsive to the issue agendas of parties from their own party family than to the issue agendas of non-family parties and that large mainstream parties are more responsive than niche parties to the common issue agenda of the other parties in the party system.