Competition between political parties is a process that unfolds over time whereas formal theories of party competition have tended to take an essentially static, or one-shot, approach. This leaves some gaps in our understanding of the dynamics of campaigning. The aim of this paper is to make up some of this gap. This is done using a differential game theory model to analyse a situation in which support for a party depends on the amount spent on marketing relative to the expenditure of the other party. One of the main results is that, even when voters are not myopic, the logic of the competition forces parties to accelerate expenditure on campaigning during the period between elections.