A microlithographic projection exposure apparatus has a measuring device, by which a sequence of measurement values can be generated, and a processing unit for processing the measurement values. The processing unit has a processing chain which includes a plurality of digital signal processors. The first digital signal processor in the processing chain is connected to the measuring device to receive the sequence of measurement values. Each subsequent digital signal processor in the processing chain is connected to a respectively preceding digital signal processor in the processing chain. The digital signal processors are programmed so that each digital signal processor processes only a fraction of the measurement values and generates processing results therefrom, and forwards the remaining fraction of the measurement values to the respective next digital signal processor in the processing chain for processing.