This work is concerned with the identification of global models for non-linear dynamical systems using multiobjective evolutionary algorithms. The identification of non-linear systems involves the processes of structure selection, parameter estimation, model performance and model validation and involves a complex solution space. Evolutionary Algorithms (EAs) are search and optimisation tools founded on the principles of natural evolution and genetics, which are suitable for a wide range of application areas. Due to the versatility of these tools, two evolutionary methods, Genetic Algorithms (GA) and Genetic Programming (GP), are investigated for use in non-linear system identification. Initially, these evolution-based approaches are used to evaluated the Akaike Information Criterion (AIC) in order to identify the best non-linear system model. However, only model size (a model structure attribute) and short time prediction error (a model performance attribute) are considered within this information criterion. GP was found to provide superior performance for this single-objective function and as a result, its use was extented to encompass multiobjective functions. MultiObjective Genetic Programming (MOGP) is applied to multiple, conflicting objectives and yields a set of candidate parsimonious and valid models which reproduce the original system behaviour at different working conditions (global models). The MOGP identification approach is applied, first, to simulated data and then to sets of observations from a real system, a Rolls-Royce gas turbine engine. The benchmark problem of the 6-Boolean Multiplexer is also introduced to demonstrate the applicability of MOGP in a domain other than system identification. Finally, MOGP is demonstrated as being a highly applicable non-linear system identification technique by addressing the identification of systems with chaotic dynamics and its ability to deal with rational system representations.