Offshore wind energy has gained widespread attention and experienced a rapid development due to the significantly increasing demand for renewable energy over the past few years. Currently, the development of offshore floating wind turbines attracts lots of attention to harvest more energy from a sustained higher speed of offshore wind away from the coastline. With stronger cyclic wind and wave loadings, the floating wind turbine could possibly experience severe fatigue damages at certain critical locations, which might lead to a catastrophic failure. Evaluating accumulated fatigue damage for a floating wind turbine during its entire lifetime, therefore, becomes essential and urgent. As demonstrated in the codes, specifications, or design practices, fatigue assessments require massive computational costs and pose challenges to numerical simulations since lots of dynamic analyses under different environmental scenarios need to be performed. To reduce the calculation cost for this time-consuming process while maintaining high accuracy, a probabilistic long-term fatigue damage assessment approach is proposed in the present study by implementing a C-vine copula model and a surrogate model. The C-vine copula model provides a multivariate dependency description for the on-site wind and wave-related environmental parameters. Two surrogate models, including the Kriging model and the artificial neural network (ANN), are implemented to efficiently predict the short-term fatigue damages at critical locations of the floating wind turbine. The proposed long-term fatigue damage assessment framework is accurate and suitable for evaluating structural long-term fatigue damages accumulated in a real environment especially when effects from more environmental parameters are to be considered. Based on surrogate models, sensitivity analyses are carried out to investigate the relative significance of each environmental parameter on short-term fatigue damages. In addition, uncertainties from short-term fatigue damages are also incorporated into the probabilistic fatigue evaluation framework to assess the accumulated longterm fatigue damages for a spar type floating wind turbine. (c) 2020 Elsevier Ltd. All rights reserved.