Evolutionary optimisation schemes have recently established themselves as an effective means of identifying dynamical systems, even when the parameter estimation problem is complicated by nonlinearity-in-the parameters and the presence of unmeasured states. In particular, such an approach to the parameter estimation problem for hysteretic systems has proved rather successful. Previous work by the authors has adopted the Differential Evolution (DE) algorithm of Storn and Price as the evolutionary algorithm of choice for the identification problem. Although the algorithm has proved very effective in the identification context, a minor disadvantage manifests itself in the need to set algorithm hyperparameters for the optimisation. The objective of the current paper is simply to present a recently-developed variant of the DE algorithm – the Self-Adaptive Differential Evolution algorithm (SADE) – which learns and adapts a subset of its own hyperparameters throughout the optimisation process. The use of the algorithm for the hysteretic system identification problem is illustrated using data from a computer model and it is shown that the algorithm provides several orders-ofmagntitude improvement on the minimisation of the problem objective function.