Provided are a computer program product, system, and method for processing a chain of a plurality of write requests including a commit wait flag and plurality of write requests, wherein each write request group includes write transactions directed to the storage. A determination is made as to whether the commit wait flag has a first value or a second value. The write requests are processed by requiring a current write request comprising one of the write requests being processed to complete before beginning to write data for a next write request following the current write request in the write request chain in response to the commit wait flag having the first value. The write requests are processed by processing the next write request before completing the current write request in response to the commit wait flag having the second value.