Abstract A circuit is called speed-independent if its nontransient behavior does not depend on the size of the delays in the different components of the circuit. We show that the class of speed-independent circuits is relatively small—in fact, very many useful circuits cannot be realized in a speed-independent design. For example, we show that there does not exist any speed-independent mod k counter for any k > 1. The results are derived using a very general model of a network which is applicable to both gate circuits and more modern MOS switch-level circuits. Furthermore, the results are also robust with respect to different delay assumptions and definitions of speed-independence.