Provided are techniques for, in response to establishing each incremental virtual copy from a source to a target, creating a target change recording structure for the target. While performing destage to a source data block at the source, it is determined that there is at least one incremental virtual copy target for this source data block. For each incremental virtual copy relationship where the source data block is newer than the incremental virtual copy relationship and an indicator is set in a target inheritance structure on the target for a corresponding target data block, the source data block is copied to each corresponding target data block, and an indicator is set in each target change recording structure on each target for the target data block corresponding to the source data block being destaged.