It is known that the mooring system response of floating production units subjected to environmental loads is nonlinear. Even though wave elevations can be assumed as Gaussian processes for short-term periods, corresponding line tension responses generally are not, due to second-order slow-drift floater motions and intrinsic nonlinearities of the system. In this work, short-term extreme responses are estimated based on two different approaches. In the first one, a number of probability distributions are fitted to the tension time histories’ peaks samples and classic order statistics is applied to determine the most probable extreme line tension corresponding to a short-time period (3-h) in order to identify the one with best performance. The effect of correlation between consecutive peaks in the extremes estimation is investigated through the one-step Markov chain condition by using a Nataf transformation-based model. In the second approach, a more robust and recently developed method named average conditional exceedance rate (ACER) is investigated, where dependencies between maxima can be easily taken into account. Additionally, effects of major parameters in dynamic analyses, such as simulation length and discretization level of the wave spectrum, are evaluated. All time-series-based extreme estimates are compared with the estimates directly obtained from a sample of epochal maxima (Gumbel method). Numerical examples cover two study cases for mooring lines belonging to Floating Production Storage and Offloading (FPSO) units installed offshore Brazil. It is shown that the consideration of dependence between peaks leads to lower extreme estimates and that both approaches return accurate results.