The conditional least squares (CLS) estimator proposed by Tj\o stheim (1986) is convenient and important for nonlinear time series models. However this convenient estimator is not generally asymptotically efficient. Hence Chandra and Taniguchi (2001) proposed a G estimator based on Godambe's asymptotically optimal estimating function. For important nonlinear time series models, e.g., RCA, GARCH, nonlinear AR models, we show the asymptotic variance of the G estimator is smaller than that of the CLS estimator, and the G estimator is asymptotically efficient if the innovation is Gaussian. Numerical studies for the comparison of the asymptotic variance of the G estimator, that of the CLS estimator and the Fisher information are also given. They elucidate some interesting features of the G estimator.