With respect to air quality standards, extreme events are usually of the most interest. Air quality standards require that the observed extreme concentration in a given time interval must not exceed a certain value. In this paper, it is shown that the measured maximum concentration in a time interval can be represented by one of three types of large asymptotic distribution of extreme value statistics. By using this statistical tool, it is possible to analyze the data and to predict the future extreme concentrations with a given probability. The theoretical background of extreme value statistics, procedure to estimate the parameters of the largest extreme value distributions and procedure to forecast future extreme events are briefly explained. The theory is applied to data obtained from two permanent stations in Istanbul. Hourly SO2 and NO, concentrations are analyzed and future largest SO2 and NO2 concentrations for the following 12 months are forecasted. It has been found that Gumbel's Type I and Type 11 extreme value distributions represent these air quality data obtained from the two stations very well. The expected maximum SO2 concentration is found to be 593.7 mg/ml and the NO2 concentration is found to be 393.4 mg/m(3) for the Alibeykoy station. The air quality exceeds the limit of EN standards for hourly SO2 concentration twice a year or in a return period of 5.77 months, and 5 times a year or in a return period of 2.6 months for the hourly NO2 concentrations. Similarly, for the Umraniye station, the expected maximum concentration is 514.5 mg/m(3) SO2 with a return period of 1.78 months and 43 7.6 mg/m(3) NO, with a return period of 5.6 months. The performed prediction suggests that preventive measures should be carried out in the future in order to meet stringent air quality standards.