What might it mean for execution of an action sequence to be controlled hierarchically? We argue that if production of a sequence can be decomposed into the execution of nested constituent subsequences then it should be characterized by two invariance principles that entail limits on the effects of context. Since the most primitive such decomposition merely partitions the stream of action into action units, these principles have wide applicability. According to low-level invariance the process that executes a constituent should not be influenced by changes in the larger constituents to which it belongs. According to high-level invariance changes in the content of a given constituent should have only local effects on these larger constituents. We report on tests of the two principles in the rapid production of brief utterances and short strings of keystrokes prescribed in advance, in which we examine the effects of sequence length, serial position, and unit size on measures of timing. The tests, which we intend to be illustrative rather than definitive, give some support to the existence of hierarchical constituents at the level of the individual stroke in typing and the individual stress group in speech, but provide little evidence for deeper hierarchical structure.