The resonant frequencies of a sinusoidally driven system are usually defined as those for which some physical response is a relative maximum. There is also a tendency to define them as frequencies for which the reactance of the system vanishes, since zero‐reactance frequencies are often approximately equal to maximum‐response frequencies and are sometimes easier to calculate. However, there are many systems for which the two types of frequencies are significantly different. There are also systems for which the reactance does not vanish in certain frequency ranges, though maximum responses still occur. It is concluded that vanishing reactance is not valid as a general criterion for resonance, and students should be warned against its use.