This paper investigates the nonlinear effects of the Least Mean Square (LMS) adaptive predictor. Traditional analysis of the adaptive filter ignores the statistical dependence among successive tap-input vectors and bounds the performance of the adaptive filter by that of the finite-length Wiener filter. It is shown that the nonlinear effects make it possible for an adaptive transversal prediction filter to significantly outperform the finite-length Wiener predictor. An approach is derived to approximate the total steady-state Mean Square Error (MSE) for LMS adaptive predictors with stationary or chirped input signals. This approach shows that, while the nonlinear effect is small for the one-step LMS adaptive predictor, it increases in magnitude as the prediction distance is increased. We also show that the nonlinear effect of the LMS adaptive predictor is more significant than that of the Recursive Least Square adaptive predictor.