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We consider the estimation of the marginal excess moment (MEM), which is defined for a random vector (X, Y) and a parameter β > 0 as E [ (X - Q X (1 - p)) + β | Y > Q Y (1 - p) ] provided E | X | β < ∞ , and where y + : = max (0 , y) , Q X and Q Y are the quantile functions of X and Y respectively, and p ∈ (0 , 1) . Our interest is in the situation where the random variable X is of Weibull-type while the distribution of Y is kept general, the extreme dependence structure of (X, Y) converges to that of a bivariate extreme value distribution, and we let p ↓ 0 as the sample size n → ∞ . By using extreme value arguments we introduce an estimator for the marginal excess moment and we derive its limiting distribution. The finite sample properties of the proposed estimator are evaluated with a simulation study and the practical applicability is illustrated on a dataset of wave heights and wind speeds. [ABSTRACT FROM AUTHOR]