Let $C$ be a closed convex subset of a Banach space which satisfies Opial's condition. We first prove that if $T:C\to C$ is asymptotically nonexpansive in the intermediate sense, the Ishikawa iteration process with errors defined by $x_1\in C,\ x_{n+1} =\alpha_n x_n +\beta_n T^ny_n +\gamma_n u_n$, and $y_n =\alpha_n'x_n +\beta_n'T^nx_n +\gamma_n'v_n$ converges weakly to some fixed point of $T$, which generalizes the result due to Tan and Xu. Further, we show that if $S$ and $T$ are both comact and asymptotically nonexpansive in the intermediate sense, the iterations $\{x_n\}$ and $\{y_n\}$ defined by $x_1\in C,\ x_{n+1} =\alpha_n x_n +\beta_n S^ny_n +\gamma_n u_n$, and $y_n =\alpha_n'x_n +\beta_n'T^nx_n +\gamma_n'v_n$ converge strongly to the same common fixed point of $S$ and $T$, which generalizes the result due to Rhoades.