The standard theory of memory consolidation posits a dual-store memory system: a fast-learning fast-decaying hippocampus that transfers memories to slow-learning long-term cortical storage. Hippocampal lesions interrupt this transfer, so recent memories are more likely to be lost than more remote memories. Existing models of memory consolidation that simulate this temporally graded retrograde amnesia operate only on static patterns or unitary variables as memories and study only one-way interaction from the hippocampus to the cortex. However, the mechanisms underlying the consolidation of episodes, which are sequential in nature and comprise multiple events, are not well-understood. The representation of learning for sequential experiences in the cortical-hippocampal network as a self-consistent dynamical system is not sufficiently addressed in prior models. Further, there is evidence for a bi-directional interaction between the two memory systems during offline periods, whereby the reactivation of waking neural patterns originating in the cortex triggers time-compressed sequential replays in the hippocampus, which in turn drive the consolidation of the pertinent sequence in the cortex. We have developed a computational model of memory encoding, consolidation, and recall for storing temporal sequences that explores the dynamics of this bi-directional interaction and time-compressed replays in four simulation experiments, providing novel insights into whether hippocampal learning needs to be suppressed for stable memory consolidation and into how new and old memories compete for limited replay opportunities during offline periods. The salience of experienced events, based on factors such as recency and frequency of use, is shown to have considerable impact on memory consolidation because it biases the relative probability that a particular event will be cued in the cortex during offline periods. In the presence of hippocampal learning during sleep, our model predicts that the fast-forgetting hippocampus can continually refresh the memory traces of a given episodic sequence if there are no competing experiences to be replayed.