Provided are a computer program product, system, and method for replication of versions of an object from a source storage to a target storage. A source retention policy indicates at least one source retention requirement to determine when to expire versions of an object at the source storage and a target retention policy indicates at least one target retention requirement to determine when to expire versions of the object at the target storage. The source and target retention requirements for versions of the object are different. The source retention policy is used to expire at least one version of the object at the source storage to satisfy the at least one source retention requirement. A number of the versions of the object maintained at the source storage and target storage differ due to the different source and target retention requirements.