Provided are a method, system, and article of manufacture for managing write requests to data sets in a primary volume subject to being copied to a secondary volume. Information indicating data sets to copy from a primary storage to a secondary storage is generated. A write request is received to write data to a target data set indicated in the information to copy from the primary storage to the secondary storage. A determination is made as to whether the write request is part of a sequential write access. The target data set and sequential data sets following the target data set are copied from the primary storage to the secondary storage. The write request to write the data to the primary storage is executed in response to receiving acknowledgment that the target data set was copied to the secondary storage.