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The block maxima method is a classical and widely applied statistical methodfor time series extremes. It has recently been found that respective estimatorswhose asymptotics are driven by empirical means can be improved by usingsliding rather than disjoint block maxima. Similar results are derived forgeneral non-degenerate U-statistics of arbitrary order, in the multivariatetime series case. Details are worked out for selected examples: the empiricalvariance, the probability weighted moment estimator and Kendall's taustatistic. The results are also extended to the case where the underlyingsample is piecewise stationary. The finite-sample properties are illustrated bya Monte Carlo simulation study.

Limit theorems for non-degenerate U-statistics of block maxima for time series