In this paper, we address the state initialization problem in recurrent neural networks (RNNs), which seeks proper values for the RNN initial states at the beginning of a prediction interval. The proposed methods employ various forms of neural networks (NNs) to generate proper initial state values for RNNs. A variety of RNNs are trained using the proposed NN initialization schemes for modeling two aerial vehicles, a helicopter and a quadrotor, from experimental data. It is shown that the RNN initialized by the NN-based initialization method outperforms the washout method which is commonly used to initialize RNNs. Furthermore, a comprehensive study of RNNs trained for multistep prediction of the two aerial vehicles is presented. The multistep prediction of the quadrotor is enhanced using a hybrid model, which combines a simplified physics-based motion model of the vehicle with RNNs. While the maximum translational and rotational velocities in the Quadrotor data set are about 4 m/s and 3.8 rad/s, respectively, the hybrid model produces predictions, over 1.9 s, which remain within 9 cm/s and 0.12 rad/s of the measured translational and rotational velocities, with 99% confidence on the test data set.