Within the scope of this thesis a photon tagging system was designed and constructed at the superconducting Darmstadt electron linear accelerator (S-DALINAC). The set-up consists of a deflecting magnet, an array of focal plane detectors, the data acquisition system and new beam-line components. The system provides tagged photons in an energy range from 6 MeV to 20 MeV with the emphasis on best possible resolution and intensity. The absolute energy resolution of photons at 10 MeV is better than 25 keV. With the current focal-plane detectors a maximum rate of tagged photons of 104/(keV s) can be achieved. An upgrade to more than 105/(keV s) with an alternative detector array is under investigation. The design values mentioned above are the requirements for planned experiments in the fields of nuclear astrophysics and nuclear structure. The most important constraints which have to be considered arise from the special demands of (γ,n) reactions above but close to the particle threshold which generates slow neutrons with energies of a few hundreds of keV. The unambiguous assignment of slow neutrons to prompt electrons is done on-line in special buffered time-to-digital converters. With a design of the data acquisition for this scenario one also covers the requirements for experiments with prompt detection of the ejectiles such as in nuclear resonance fluorescence and (γ,n) far above the threshold. This photon tagging system enables to measure (γ,x) cross sections as a function of excitation energy and decay patterns after particle evaporation. It is an important extension to the high-flux activation experiments and the nuclear resonance fluorescence experiments below the threshold with untagged bremsstrahlung.