In the mammalian brain, a newly acquired memory depends on the hippocampus for maintenance and recall, but over timethe neocortex takes over these functions, rendering the memory hippocampus-independent. The process responsible forthis transformation is called systems memory consolidation. Interestingly, retrieval of a well-consolidated memory cantrigger a temporary return to a hippocampus-dependent state, a phenomenon known as systems memory reconsolidation.The neural mechanisms underlying systems memory consolidation and reconsolidation are not well understood. Here,we propose a neural model based on well-documented mechanisms of synaptic plasticity and stability and describe acomputational implementation that demonstrates the models ability to account for a range of findings from the systemsconsolidation and reconsolidation literature. Based on the computational model, we derive a number of predictions andsuggest experiments that may put them to the test.