In the context of structural performance assessment, several studies have employed fragility curves and surfaces to evaluate the damage probability for predefined intensity levels of a single or multiple hazards. Further, some of these studies have considered the use of tuned mass dampers (TMDs) to reduce the response of structures under wind or seismic loading. In this work, fragility curves and surfaces of a slender structure fitted with TMDs subjected to turbulent wind and seismic loading alone and simultaneously are developed. For the numerical analyses, simulated records for wind and earthquake ground motion are considered. For the development of fragility curves and surfaces, three damage states that include local and global behavior of the structure are considered. The analysis results indicate that, for the structure considered, higher probability of damage is found from wind action than from earthquake, and that an important reliability enhancement is achieved with the use of TMDs.