Hollow Cathodes (HCs) are of primary importance in the field of electric space propulsion, being used as electron sources in ion and Hall-effect thrusters. Hence, their lifetime is a key factor in all these applications. HCs have demonstrated the capability of providing up to 30,000 hours of operation, whereas no direct experimental data exist above this limit. The importance of HC lifetime is a growing issue for deep space missions using propulsive systems based on ion or Hall-effect thrusters that may require longer lifetimes than those demonstrated up to now. To address these concerns about HCs and to prove the suitability of an ion thrusters based solar electric propulsion subsystem for future high-impulse missions (such as Bepi Colombo), a model able to predict the HC lifetime is needed. The model that has been developed in this thesis consists of three parts: a barium oxide depletion model, a low work function surface coverage model and a plasma update procedure to calculate the effects that a change in the insert surface work function will produce on the cathode plasma. The barium-oxide depletion model has been validated by comparing its results with experimental measurements performed at QinetiQ and NASA, showing a good quantitative agreement. The low-work function surface coverage model is the first of its kind to include the effect of ion bombardment. The plasma update procedure, even if semi-empirical, is able to produce results that are in good agreement with the measurements. Using these three models the lifetime of the NSTAR hollow cathode has been simulated, yielding predictions that are in good agreement with the theoretical expectations.