The control framework of hierarchical consistency of timed discrete-event systems (TDES's) is investigated in a standard two-level hierarchy. Real-time concepts and the associated theoretical results supporting consistent TDES hierarchies are developed. Where the given low-level system model of the hierarchy possesses time fidelity, a consistency version that assures time fidelity of the high-level system model is also developed. Importantly, this version furnishes a sound real-time high-level specification design foundation for hierarchical control. An example illustrates the new time-fidelity control foundation. Given that in general, a given two-level TDES hierarchy is not hierarchically consistent between the levels, the structural existence and synthesis of the sufficiency structure for hierarchical consistency is investigated. Both the timed versions of hierarchical consistency - without and with output-time fidelity guarantee - are successively treated. The abstraction or output-system refinement procedures for the version without output-time fidelity guarantee are first developed for a class of TDES hierarchies under mild output-system design restrictions. The abstraction methods for the version with output-time fidelity are then developed for a subclass 'linearly' structured under further output-system design restrictions. A detailed example explains and illustrates the use of an overarching method developed.