Nonlinear averaging methods are applied to analyze reduced-order adaptive controllers. An adaptive control system with two adjustable parameters and arbitrary unmodeled dynamics is studied. It is shown that when the reference input consists of only one sinusoid, the averaged system almost always possesses a unique equilibrium. When the input consists of several sinusoids, the averaged system may possess Several equilibria, which may or may not be stable. It is shown that the adaptive system may be unstable, even if it is stable for the frequency components separately.