Modelling extreme values from an environmental time series requires an extreme-value theory model which can handle dependent observations. A method of filtering the original time series to obtain independent extremes is presented. The resulting extremes are then modelled using an extension of suggested ideas*. Here the limiting joint Generalized Extreme Value distribution for the r largest order statistics is considered; whereas others^** ** Smith (1986). used the corresponding Gumbel distribution. Various tests of fit of the model are discussed, with a detailed analysis of how to test for dependence between extremes in the original sequence. An additional method of using data from neighbouring sites to improve the estimation is suggested. The procedures and tests are illustrated by an application to the sea levels at Lowestoft and Great Yarmouth.