This thesis deals with the application of modern identification techniques to model the dynamic relationship between the fuel flow and shaft speeds of a Rolls Royce aircraft gas turbine. It is motivated by the desire to exploit recent advances in modelling linear and nonlinear systems and the need to investigate the suitability of various model representations in nonlinear gas turbine modelling. The first part of the thesis deals with linear gas turbine modelling, with the aim of estimating models which can be used to verify the linearised thermodynamic models derived from the engine physics, at different shaft speeds. A detailed analysis of the engine data is presented and linear engine models are identified at different operating points using time- and frequency-domain techniques. The influence of noise and nonlinearities on the estimated models is studied and it is shown that the use of multisine signals and frequency-domain techniques is particularly suited to this problem, since the derived continuous-time s-domain models can be directly compared with the linearised thermodynamic models. It is also shown that discrete models estimated in the time domain have excellent approximation capabilities but are not suited for the validation of the thermodynamic models since their modes are uncertain and they sometimes result in modes which do not have a continuous-time counterpart. The second part of the thesis deals with the application of several nonlinear system representations to model the nonlinear relationship between the fuel flow and shaft speeds of the gas turbine. Data is analysed in both time- and frequency-domain to gain information about the engine nonlinearity, and several nonlinear model representations are presented along with popular estimation algorithms. Nonlinear models for each shaft were then estimated and the performance of these models was demonstrated by their ability to approximate measured engine data. It is shown that the nonlinear relationship between the fuel flow and shaft speed can be modelled using a Wiener structure, a NARMAX structure or a neural network. Several issues concerning signal design and prior knowledge of the nonlinearity in a system are also discussed and a number of recommendations are made for future gas turbine modelling and testing. This thesis is a contribution to the further application of multifrequency signals and time- and frequency-domain techniques to the identification of linear and nonlinear models for aircraft gas turbines. While this work was applied to a gas turbine, these techniques can be applied to a range of industrial applications that deal with system testing and modelling.