Mathemathical and physical modelling only provide approximate description of the true nature of a dynamic system. The higher the precision of the model the more likely it becomes analytically intractable and, therefore, empirical models or black box models are used. When dynamic systems are considered as black box models, almost no prior knowledge about the system is considered. Deep Gaussian Processes, which use hierarchical structure to provide adequate identification of very complex systems, can be used to identify the mapping between the system input and output values. With the given mapping function we can then provide a one-step ahead prediction of the system output values, together with its uncertainty, which can be advantageously used. In this paper we use deep Gaussian Processes to identify a dynamic system and present its advantages by studying two cases. In the first illustrative case we successfully identify the dynamic properties of a nonlinear oscillating mass, while in the second, more realistic and complex case, we study one-step ahead prediction of air temperature in the atmospheric surface layer.