The extreme values of many parameters measured by the space science community are important because they have a significant impact on human activities. For example, estimates of extreme radiation belt fluxes, plasma temperatures, and solar particle events must be considered when designing spacecraft, and extreme auroral currents must be considered when designing ground-based electric power systems. The mathematical tools that have been developed to address such problems are known as the statistics of extreme values. Here these tools have been applied to three data sets in order to determine if extreme value parametric models can accurately describe space weather parameters. The three examples chosen are (1) the annual maxima of the magnetic index Ap for the years from 1932 to 1997, (2) the annual maxima of the daily average flux of >60 MeV protons measured by the Interplanetary Monitoring Platform spacecraft from 1973 to 1998, and (3) the exceedances of the flux over a threshold of 104 el cm-2 s-1 sr-1 of >2 MeV electrons at geosynchronous orbit measured by the GOES spacecraft from 1986 to 1999. The parameters for each model were determined using the maximum likelihood estimate. The validity of each model was tested using a quantile-quantile (Q-Q) plot. In each case an excellent fit to the extremes of the sample distribution function is given by an appropriate extreme value distribution function. These extreme value distribution functions were also used to estimate the 50- and 100-year values for each data set. The results show that the extreme values observed to date are not unusual in that they are well fit by extreme value models. They also show that larger values than observed to date can be expected for each of the parameters during any 100-year period. ¿ 2001 American Geophysical Union