We investigate what computational mechanisms give rise to the nonlinearity of complex cell responses in the primary visual cortex. Complex cells are characterized by their nonlinear spatial properties such as spatial phase invariance and nonlinear spatial additivity. We carried out network simulations to estimate the second-order Wiener-like kernels for several different models. Models with nonlinear spatial pooling of simple-cell-like linear subunits reproduce the second-order kernels in good agreement with physiologically estimated kernels, while models without the pooling mechanism fail to reproduce the kernel. The results support the cascade mechanism consisting of simple cells' local feature extraction followed by spatial pooling.