This work deals with the analysis and prediction of the behavior of a Gas Turbine (GT), the Mitsubishi single shaft Turbo-Generator Model MS6001, which has a 30MW generation capacity. GTs such as this are of great importance in industry, as drivers of gas compressors for power generation. Because of their complexity and their execution environment, the failure rate of GTs can be high with severe consequences. These units are subjected to transient operations due to starts, load changes and sudden stops that degrade the system over time. To better understand the dynamic behavior of the turbine and to mitigate the aforementioned problems, these transient conditions need to be analyzed and predicted. In the absence of a thermodynamic mathematical model, other approaches should be considered to construct representative models that can be used for condition monitoring of the GT, to predict its behavior and detect possible system malfunctions. One way to derive such models is to use data-driven approaches based on machine learning and artificial intelligence. This work studies the use of state-of-the-art genetic programming (GP) methods to model the Mitsubishi single shaft Turbo-Generator. In particular, we evaluate and compare variants of GP and geometric semantic GP (GSGP) to build models that predict the fuel flow of the unit and the exhaust gas temperature. Results show that an algorithm, proposed by the authors, that integrates a local search mechanism with GP (GP-LS) outperforms all other state-of-the-art variants studied here on both problems, using real-world and representative data recorded during normal system operation. Moreover, results show that GP-LS outperforms seven other modeling techniques, including neural networks and isotonic regression, confirming the importance of GP-based algorithms in this domain.