Across vertebrate species, sleep consists of repeating cycles of NREM followed by REM. However, the respective functions of NREM and REM states, as well as their stereotypic cycling pattern, are not well understood. Here, using a simplified biophysical network model, we show that NREM and REM sleep can play differential and critical roles in memory consolidation primarily regulated, based on state-specific changes in cholinergic signaling. Within this network, decreasing and increasing muscarinic acetylcholine (ACh) signaling during bouts of NREM and REM, respectively, differentially alter neuronal excitability and excitatory/inhibitory (E/I) balance. Learning was modeled in the network as increased firing in a subpopulation of excitatory neurons in the network (engram neurons) during a high-ACh wake-like stated. During subsequent NREM, ACh-regulated current (m-current) causes deactivation of inhibitory neurons, leading to network-wide disinhibition and bursts of synchronized activity led by firing in engram neurons. Together, these features strengthen connections from the original engram neurons to less-active excitatory network neurons, which become incorporated into the memory engram. In contrast, when m-current is blocked during subsequent REM, an increase in network inhibition suppresses firing in all but the most-active excitatory neurons, leading to competitive elimination of newly-recruited neurons from the memory trace. We find that an iterative sequence of state-specific activations during NREM/REM cycling is essential for memory storage in the network, serving a critical role during simultaneous consolidation of multiple memories. When sleep cycles were reversed (i.e., REM followed by NREM), or one longer cycle was substituted for multiple shorter cycles, neither of two memories is successfully consolidated. Together these results provide a mechanistic, testable hypothesis for the respective roles of both NREM and REM sleep, and their universal timing, in memory consolidation.