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Many system-on-chip (SOC) integrated circuits today contain hierarchical (parent) cores that have multiple levels of design hierarchy involving "child cores". Hierarchy imposes a number of constraints on the manner in which tests must be applied to parent cores and their child cores. However, most prior work on wrapper design, test access mechanism (TAM) optimization, and test scheduling are hierarchy-oblivious, i.e., these techniques treat all cores in an SOC at the same level of hierarchy. We first show that wrappers, TAMs and test schedules designed for non-hierarchical SOCs are not valid for SOCs with hierarchical cores. We next present two approaches for the efficient testing of SOC with hierarchical cores. In the first approach, an existing wrapper design is modified such that that all constraints imposed by the hierarchy are satisfied and full flexibility is provided for TAM optimization and test scheduling. The second approach is based on a hierarchy-aware wrapper architecture for parent cores that operates in two disjoint modes for the testing of parent and child cores. We show how an existing test-architecture design algorithm can be adapted for use with these two methods. Results for the ITC'02 SOC Test Benchmarks show that the first approach offers lower test application times while the second approach requires less area overhead.