We present three different approaches to modelling extreme values of daily air pollution data. We fitted a generalized extreme value distribution to the monthly maxima of daily concentration measures. For the exceedances of a high threshold depending on the data, the parameters of the generalized Pareto distribution were estimated. Accounting for autocorrelation, clusters of exceedances were used. To obtain information about the relationship of the exceedance of the air quality standard and possible predictors we applied logistic regression. Results and their interpretation are given for daily average concentrations of ozone and nitrogen dioxide at two monitoring sites within the city of Munich.