A motion cueing algorithm (MCA) is employed to transform the linear and angular motion signals generated from a motion simulator without violating the physical and dynamical boundaries of the motion platform. In this respect, the accurate prediction of the motion scenarios is essential to enhance the efficiency of the MCA using prepositioning or time-varying reference model predictive control. While a recent approach that utilizes a feedforward neural network (NN) to forecast the motion scenarios is useful, the feedforward NN model has only forward dynamics relating to the signals without any feedback loop. In this article, a time-delay feedforward NN, a recurrent NN, and a nonlinear autoregressive (NAR) models with three different training procedures, i.e., Levenberg–Marquardt, Bayesian regularization, and scaled conjugate gradient, are exploited to predict the motion scenarios. As the NAR model employs the historical signals as the inputs, it can predict the motion scenarios with higher accuracy rates. Based on the series of empirical evaluations, NAR trained with Levenberg–Marquardt is able to outperform the other two counterparts in producing more accurate predictions of the motion signals. The NAR method has a lower computational load as compared with that of the recurrent NN, facilitating its real-time application. In addition to the MCA, the NAR method can be employed in other areas, including autonomous vehicles and motion sickness studies. It can also be easily implemented for air, sea, and/or land vehicle simulators for training purposes in virtual reality environments.