The ZEUS detector has a high-resolution uranium calorimeter which can be used to identify leptons. The segmentation of the calorimeter is sensitive to the longitudinal and transverse particle energy deposition within the calorimeter. The phase space probability method is used to identify muons. It is based on Monte Carlo simulations, with the help of which we construct the muon probability function in the multi-dimensional phase-space of the calorimeter signals. A feed-forward neural network is used to identify electromagnetic showers. Both methods separate leptons with high efficiency and a low level of hadron contamination.