An apparatus, program product and method track concurrent uses of a computer program across a plurality of logical partitions in a logically partitioned computer, such that a decision as to whether to grant or deny a request to use the computer program in a particular logical partition may be made based upon whether the requested use, coupled with other uses in other logical partitions in the computer, would violate a concurrent use software license associated with the computer program. As such, the license restrictions of a concurrent use software license can be enforced on a logically partitioned computer regardless of the particular logical partitions within which a computer program executes.