Dual-process theories of episodic memory state that retrieval is contingent on two independent processes: familiarity (providing a sense of oldness) and recollection (recovering events and their context). A variety of studies have reported distinct neural signatures for familiarity and recollection, supporting dual-process theory. One outstanding question is whether these signatures reflect the activation of distinct memory traces or the operation of different retrieval mechanisms on a single memory trace. We present a computational model that uses a single neuronal network to store memory traces, but two distinct and independent retrieval processes access the memory. The model is capable of performing familiarity and recollection-based discrimination between old and new patterns, demonstrating that dual-process models need not to rely on multiple independent memory traces, but can use a single trace. Importantly, our putative familiarity and recollection processes exhibit distinct characteristics analogous to those found in empirical data; they diverge in capacity and sensitivity to sparse and correlated patterns, exhibit distinct ROC curves, and account for performance on both item and associative recognition tests. The demonstration that a single-trace, dual-process model can account for a range of empirical findings highlights the importance of distinguishing between neuronal processes and the neuronal representations on which they operate.