Recently, a new branch of astronomy has emerged following the detection of ultra-high energy (UHE) γ-ray emission from Cygnus X-3 by Samorski and Stamm (1983). This discovery was made using the extensive air shower (EAS) array of the University of Kiel, Germany. Such arrays are designed to detect EAS, the cascades of secondary particles (mainly electrons and protons), which are generated in the atmosphere by the interaction of cosmic ray nuclei of energy greater than ˜ 1015 eV. These arrays are also sensitive to EAS initiated by primary γ-rays and, depending on their design, have angular resolutions as good as the SAS-II and COS-B γ-ray telescopes which operated at ˜ 100 MeV energies. At present, there is no effective way to veto proton or nucleus-initiated EAS and so one must look for a significant excess of EAS from within a cone of resolution centred on a suspected source direction.