This paper provides a stability analysis of a class of acoustic noise control algorithms by showing that the adapted models have more in common with nonlinear, finite impulse response (FIR) equation error models than with the infinite impulse response (IIR) output error models they superficially resemble. Stability results from the adaptive control literature are applied to show global stability in the noise free case, and to show exponential stability when the input is persistently excited. The latter demonstrates a robustness to mismodeling errors, disturbances such as noises, and allows results to be applied to the tracking of time-varying systems.