In this paper, we apply the principles of information theory that relate to the definition of nonlinear predictability, which is a measure that describes both the linear and nonlinear components of a system. By comparing this measure to a measure of linear predictability, one can assess whether a given system has a strong nonlinear or a strong linear component. This provides insights as to whether the system should be modelled by a nonlinear model or by a linear model. We apply these ideas to a known dynamical system and to a time series that describe the transitions in atmospheric circulation.