In this paper, we propose a new mathematical model of retrieval of intentions from long-term memory. We model retrieval as a stochastic race between a plurality of potentially relevant intentions stored in long-term memory. Psychological theories are dominated by two opposing conceptions of the role of memory in temporally extended agency – as when a person has to remember to make a phone call in the afternoon because, in the morning, she promised she would do so. According to the Working Memory conception, remembering to make the phone call is explained in terms of the construction and maintenance of intentions in working-memory. According to the Long-Term Memory conception, we should explain the episode in terms of an ability to store intentions in long-term memory. The two conceptions predict different processing profiles. The aim of this paper is to present a new mathematical model of the type of memory mechanism that could realise the long-term memory representations of intentions necessary for the Long-Term Memory conception. We present and illustrate the formal model and propose a new type of experimental paradigm that could allow us to test which of the two conceptions provides the best explanation of the role of memory in temporally extended agency.