Recent neuroimaging studies demonstrate that remembering the past and imagining the future rely on the same core brain network. However, findings of common core network activity during remembering and imagining events and increased activity during future event simulation could reflect the recasting of past events as future events. We experimentally recombined event details from participants' own past experiences, thus preventing the recasting of past events as imagined events. Moreover, we instructed participants to imagine both future and past events in order to disambiguate whether future-event-specific activity found in previous studies is related specifically to prospection or a general demand of imagining episodic events. Using spatiotemporal partial-least-squares (PLS), a conjunction contrast confirmed that even when subjects are required to recombine details into imagined events (and prevented from recasting events), significant neural overlap between remembering and imagining events is evident throughout the core network. However, the PLS analysis identified two subsystems within the core network. One extensive subsystem was preferentially associated with imagining both future and past events. This finding suggests that regions previously associated with future events, such as anterior hippocampus, medial prefrontal cortex and inferior frontal gyrus, support processes general to imagining events rather than specific to prospection. This PLS analysis also identified a subsystem, including hippocampus, parahippocampal gyrus and extensive regions of posterior visual cortex that was preferentially engaged when remembering past events rich in contextual and visuospatial detail.