This project presents the theoretical background for calculating the long-term extreme response of pontoon-style floating bridges. Research into surrogate models for the long-term extreme response is given special attention, and various simulations of the response of a simplified bridge are carried out to provide a comparison of the different theories presented. Firstly, the modelling of wind generated waves is discussed. Two major environmental parameters, the significant wave height and the mean wave peak period, are necessary for the models. The joint probability distribution of the occurrence of sea states characterised by these parameters is presented. The finite element model set-up for a floating bridge is shown, as is the integration of the fluid-structure interaction into the finite element model. The dynamic analysis in of the floating bridge in the frequency domain is derived. In combination with a given sea state, this allows the calculation of the short-term response of the bridge – the calculation is a computationally expensive task. The statistical model for the long-term extreme response of a floating bridge is derived. The extremely computationally expensive nature of this task leads to the development of inverse first and second order reliability methods, which treat the long-term extreme response calculation as an optimisation problem to be solved with gradient based methods. To avoid calculating gradients, surrogate models are another possible approximation method for the long-term extreme response. Both surrogate models based on Kriging and thin plate splines show similar and promising results, which concur with the outcome IFORM and ISORM, and with a rough full long-term extreme response calculation, based on the simulations in this project. Surrogate models show high potential for modelling the long-term extreme response of bridges due to their accuracy and relatively low computational effort.