The paper initiates the investigation of nonlinear differential systems with input unmodeled dynamics. A motivating example shows that they can result in a destabilizing effect even in their simplest form. A dynamic nonlinear damping design is introduced to bound uncertainties affecting the parameter update law. Its stabilizing effect is proved in the scalar case. It is further extended to higher order systems via integrator backstepping. If the uncertain parameter \(\mu\) is sufficiently small then the solutions are globally bounded and converge to a neighborhood of the origin with radius proportional to \(\mu\) and independent of the initial condition. Moreover, for even smaller \(\mu\), the origin is globally asymptotically stable.