We studied nitrogen doped ZnSe and ZnSSe epilayers grown on p-GaAs substrates by MBE using deep-level transient spectroscopy and admittance spectroscopy. Three major hole traps T1-T3 were observed with energy levels at 0.11, 0.46, and 0.56 eV from the valence band. Similar energy levels were observed in ZnSSe:N except that T1 was at 0.12 eV from the valence band. We attribute T1 to a nitrogen acceptor which controls the p-type conduction in the materials. A crude estimation of the 0.11 eV trap concentration obtained from the data shows correlation with the free carrier concentration due to nitrogen. The two remaining levels may originate from the nitrogen doping process.