Current evidence provides support for the idea that time is mentally represented by spatial means, i.e., a left-right mental timeline. However, available studies have tested only factual events, i.e., those which have occurred in the past or can be predicted to occur in the future. In the present study we tested whether past and future potential events are also represented along the left-right mental timeline. In Experiment 1 participants categorized the temporal reference (past or future) of either real or potential events and responded by means of a lateralized (left or right) keypress. Factual events showed a space-time congruency effect that replicated prior findings: Participants were faster to categorize past events with the left hand and future events with the right hand than when using the opposite mapping. Crucially, this also ocurred for potential events. Experiment 2 replicated this finding using blocks of trials comprising only potential events. In order to assess the degree of automaticity of the activation of the mental timeline in these two kinds of events, Experiment 3 asked participants to judge whether the expressions referred to factual or potential events. In this case, there was no space-time congruency effect, showing that the lateralized timeline is active only when relevant to the task. Moreover, participants were faster to categorize potential events with the left hand and real events with the right hand than when using the opposite mapping, suggesting for the first time a link between the mental representations of lateral space and potentiality.