Conformance testing focuses on checking whether an implementation under test (IUT) behaves according to its specification. Typically, testers are interested in performing targeted tests that exercise certain features of the IUT. This intention is formalized as a test purpose. The tester needs a "strategy" to reach the goal specified by the test purpose. Also, for a particular test case, the strategy should tell the tester whether the IUT has passed, failed, or deviated from the test purpose. In [8] J?eron and Morel show how to compute, for a given finite state machine specification and a test purpose automaton, a complete test graph (CTG) which represents all test strategies. In this paper, we consider the case when the specification is a hierarchical state machine and show how to compute a hierarchical CTG which preserves the hierarchical structure of the specification. We also propose an algorithm for an online test oracle which avoids a space overhead associated with the CTG.