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Experimental data shows that permanent magnet stepper motors can spontaneously reverse their direction of rotation when controlled in full step, open-loop mode. This paper shows that the reversal of speed can be explained, and that the reverse speed is equal to three times the forward speed. A linear approximation of the motor dynamics predicts that reverse running will arise when the undershoot of the single-step response exceeds 50% (or when the damping factor is less than 0.11). The observations of this paper suggest a revision of the conventional explanation that resonance problems occur because of high positive velocity at the stepping time. Instead, the data and the analysis of the paper suggest that resonance problems, including stalling and speed reversal, occur due to the growth of the undershoot in the response to repeated steps.