Adaptive proportional-integral-derivative (PID) controllers are used to control model-following nonlinear systems with second order deminant dynamics. An Adaptive PID-based controller is designed which drives the difference (error) between a process response and a desired model output to zero. The design approach is based on the model reference adaptive control technique. Lyapunov stability theory is used to analyze asymptotic stability of the error system and to obtain controller tuning rules. The proposed design scheme and the resulting tuning rules are computed and justified for nonlinear time-varying and/or uncertain plants where the dominant dynamics are of second order. The uncertain nonlinearities are assumed to be bounded by a known constant or a function of the plant output and its derivative. The disturbances in the system are dealt with in the design scheme and they are assumed to be bounded by a known parameter. It is shown that the error approaches zero asymptotically at a rate constrained by the desired model's characteristics. Simulation results for various nonlinearities show that the proposed tuning technique performs very well.