Physical-law based models are widely utilized in the aerospace industry. One such use is to provide flight dynamics models for use in flight simulators. For human-in-the-loop use, such simulators must run in real-time. Due to the complex physics of rotorcraft flight, to meet this real-time requirement, simplifications to the underlying physics sometimes have to be applied to the model, leading to model response errors in the predictions compared to the real vehicle. This study investigated whether a machine-learning technique could be employed to provide rotorcraft dynamic response predictions, with the ultimate aim of this model taking over when the physics-based model's accuracy degrades. In the current work, a machine-learning technique was employed to train a model to predict the dynamic response of a rotorcraft. Machine learning was facilitated using a Gaussian Process (GP) non-linear autoregressive model, which predicted the on-axis pitch rate, roll rate, yaw rate and heave responses of a Bo105 rotorcraft. A variational sparse GP model was then developed to reduce the computational cost of implementing the approach on large data sets. It was found that both of the GP models were able to provide accurate on-axis response predictions, particularly when the input contained all four control inceptors and one lagged on-axis response term. The predictions made showed improvement compared to a corresponding physics-based model. The reduction of training data to one-third (rotational axes) or one-half (heave axis) resulted in only minor degradation of the GP model predictions.