In this paper, we apply methods of nonlinear dynamics to study the behavior of a microelectromechanical oscillator. We show how the analysis predicts the appearance of a devil's staircase-like relationship between frequencies, but also show how the output frequency of the oscillator, and hence the devil's staircase, may not be uniquely determined. Both of these features - the sequence of steps corresponding to different output frequencies and the fact that the output frequency may not be uniquely defined for a given set of parameters - have a direct bearing on the ease with which a designer can produce an useful oscillator of this form.