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The Hadron Elektron Ring Anlage (HERA) is a unique 30GeV electron 820 GeV proton collider presently under construction at DESY in Hamburg, Germany. HERA is not a conventional collider, because it is asymmetric: neither the centre of mass frame nor the target frame coincide with the laboratory frame. The time interval between beam crossings (96 ns) is very short. In chapter 2, the HERA parameters and the HERA physics potential are discussed. ZEUS is a detector for this electron-proton collider. In chapter 3, the ZEUS detector is described with the emphasis on the high resolution calorimeter and on data acquisition and triggering. In chapter 4, the second level calorimeter trigger algorithm is explained and the implementation is discussed. The performance of the trigger algorithm implemented in this transputer environment has been tested using Monte Carlo events. In chapter 5, the Monte Carlo event generators, that have been used for the studies in the thesis, are discussed. In the last chapter (6), several important results of the second level calorimeter trigger processor algorithm are presented.