Provided are a computer program product, system, and method for updating change information for current copy relationships when establishing a new copy relationship having overlapping data with the current copy relationships. A first copy relationship indicates changed first source data to copy to first target data. An establish request is processed to create a second copy relationship to copy second source data in to second target data. A second copy relationship is generated, in response to the establish request, indicating data in the second source data to copy to the second target data. A determination is made of overlapping data units in the first source data also in the second target data. Indication is made in the first copy relationship to copy the overlapping data units. The first source data indicated in the first copy relationship is copied to the first target data, including data for the overlapping data units.