The ZEUS experiment will have a three-level triggering system. The first two level involve the local processing of component data. The third level will make a decision based on the global information from an event. It is designed to accept events at 100 Hz (10 Mbyte/s) and reduce this to around 3 Hz. Furthermore, we require that the third-level processors should be Fortran programmable and have a development enviroment that allows the utilization of the offline analysis code. © 1989.