Extreme precipitation events have significant environmental consequences because they may cause considerable damages to urban as well as rural areas. The aim of this work is to construct a threshold model which will describe the exceedances over a threshold for the daily precipitation totals over Athens, Greece. The data used are daily precipitation totals recorded at the National Observatory of Athens, for a 115-year period (1891–2005). <br><br> The generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. The threshold of <i>u</i>=15.8 mm (10% upper limit) is used for the construction of the optimal return level function.