A nonvolatile memory system comprises a nonvolatile memory device including a plurality of memory blocks. The nonvolatile memory system includes a memory controller, which can control the nonvolatile memory device, and manage start and end reception times of data of each of the memory blocks. The memory controller can cause at least one of the memory blocks to be physically erased based on the managed start and end reception times. A data eliminating unit can physically erase one or more target blocks from among the memory blocks based on a block timetable in response to a data elimination command having a reference time received from a host. An operation method of a nonvolatile memory system can include selecting one or more target blocks for physical erasure in response to the data elimination command, and physically erasing the selected target blocks.