This thesis investigates the use of Multifidelity and Stochastic Polynomial Chaos Expansion for the assessment of fatigue damage in Floating Offshore Wind Turbine (FOWT) mooring systems. Specifically, the work aims to improve efficiency in providing uncertainty quantification, a probabilistic approach to computer experiments, by balancing prediction accuracy with computational cost. This is crucial for the design and analysis of complex FOWT configurations, where high-fidelity simulations are expensive. The research adopts two approaches: multifidelity (MF) modeling and Generalized Lambda Models (GLaM). While assuming an underlying polynomial structure in the data already provides a speed-up over conventional Monte Carlo estimates. The MF framework builds further on this Polynomial Chaos Expansion (PCE) by employing multiple models of varying resolution, from computationally inexpensive approximations to more accurate versions of the same solvers. Certain optimizations are applied within this method, sparse basis selection, Gaussian process regression, and basis adaptivity, which enable further speed-up and improved accuracy. In addition, when the seed is not fixed (i.e., when the stochastic nature of the problem is preserved), GLaMs are used to approximate the entire output probability distributions. Once trained, these PCE models also allow straightforward sensitivity analysis of the input-output relationships. The primary quantity of interest is mooring line fatigue damage, which results from the cyclic environmental loading experienced by the FOWT. Input uncertainty arises from environmental parameters such as wind speed, wave height, and peak period. Since wind and waves are correlated, their joint distributions are modeled using copulas. Validation is performed using the irregular Ackley function as a benchmark, alongside two realistic mooring case studies that compare quasi-static (MoorPy) and dynamic (MoorDyn) models, and investigate the impact of simulation duration on the fidelity hierarchy. Results for the Ackley benchmark confirm that the MF algorithm captures uncertainty effectively and matches the accuracy of single high-fidelity surrogates, while reducing computational cost, provided the polynomial order and truncation norm are tuned to balance bias and variance. Initial mooring studies show that quasi-static models replicate mean tensions but systematically underpredict fatigue damage. While the MF framework shows promising results for these mooring models, further investigation is needed to address and improve its limitations. The MF approach provides comparable prediction accuracy and slightly reduces the number of required dynamic samples for simpler configurations such as fairlead motion, but its performance degrades in more complex coupled two-dimensional FOWT simulations, where low-fidelity surrogates fail to capture essential coupled dynamics, limiting the effectiveness of MF corrections. Similarly, fidelity hierarchies based solely on varying simulation durations show limited benefit and require further refinement. Overall, with the added cost of the low-fidelity model, there is no clear cost benefit. Results from the GLaM framework also remain subject to further investigation due to limited time.