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Results of microwave radar Doppler spectra from 1-D nonlinear ocean surface at moderate- and low-grazing angles are calculated by the composite surface scattering model. For the large-scale undulating surface description, the narrow-band Lagrange model is used, which takes into account the vertical and horizontal skewnesses. Moreover, the shadow and the curvature effects of large-scale waves on the Doppler spectra are also considered in our calculations. Comparisons of computed curves with experimentally measured Doppler spectra at different incidence angles and at various wind speeds show that the simulated results can fit the measured data well at moderate incident angles. From the simulations, we also find that the hydrodynamic modulation and the horizontal skewness of the large-scale waves can induce remarkable influence on Doppler shift. In addition, when the shadow and the curvature effects of large-scale waves are considered in the calculations, the Doppler shifts grow more quickly and the spectral widths become narrower at low-grazing angles, and this is consistent with the numerical results given by Toporkov in the nonlinear surface case. The conclusions obtained in this work seem promising for better understanding the properties of time-dependent radar echoes from oceanic surfaces.