It has been established that currently available adaptive control algorithms may become unstable in the presence of high frequency unmodeled dynamics and additive sinusoidal disturbances. In such nonlinear dynamic adaptive control system ,there exist two infinite-gain operators which can cause the loop gains to increase without bound. Such unbounded parameters would likely cause instability. These problems can be alleviated by using a proposed model reference adaptive algorithm with bounded gains. In this paper, the mechanism of disturbance instabilities is investigated. The modified algorithm uses a limiter for the controller gains to prevent the unbounded drift. The limiting values of the proposed limiter, can be estimated analytically by applying stability criteria for linear control systems,to the linearized model of the controlled plant. The proposed adaptive controller is tested by simulation. Simulation results show the algorithm to be capable of ensuring stability of the adaptive control system , in the presence of sinusoidal disturbances.