Memory system and processor system

A memory system connected to a processor is described. The memory system includes a volatile first storage section, a nonvolatile second storage section having a smaller storage capacity than that of the first storage section, and a storage control section that performs control to store data sets in the second storage section. Each of the data sets including data written in the first storage section in response to a write command from the processor, address information indicating a write destination in the first storage section, and address information indicating a write destination in a nonvolatile third storage section to which the data written in the first storage section is to be written back.