Recurrent Neural Networks (RNNs) can encode rich dynamics which makes them suitable for modeling dynamic systems. To train an RNN for multi-step prediction of dynamic systems, it is crucial to efficiently address the state initialization problem, which seeks proper values for the RNN initial states at the beginning of each prediction interval. In this work, the state initialization problem is addressed using Neural Networks (NNs) to effectively train a variety of RNNs 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 state of the art. Further, a comprehensive study of RNNs trained for multi-step prediction of the two aerial vehicles is presented. The multi-step 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 dataset are about 4 m/s and 3.8 rad/s, respectively, the hybrid model produces predictions, over 1.9 second, which remain within 9 cm/s and 0.12 rad/s of the measured translational and rotational velocities, with 99\% confidence on the test dataset