  The ZEUS detector at HERA has been supplemented with a presampler detector in
front of the forward and rear calorimeters. It consists of a segmented
scintillator array read out with wavelength-shifting fibers. We discuss its
desi gn, construction and performance. Test beam data obtained with a prototype
presampler and the ZEUS prototype calorimeter demonstrate the main function of
this detector, i.e. the correction for the energy lost by an electron
interacting in inactive material in front of the calorimeter.
