We propose a multistage stochastic model to explain data on the kinetics of target cell lysis by cytotoxic T lymphocytes in multicellular conjugates. A novel feature of our model is that we explicitly consider both the lethal hitting stage and the target cell disintegration stage of the cytolytic process. Further, we allow for the possibility that target cell disintegration is itself a complex process composed of many events. The comparison of our model with the data of other investigators suggests that cytotoxic T cells deliver lethal hits at random to undamaged target cells. Having received a lethal hit, the target cell disintegrates over a variable length of time. The disintegration times of target cells from different conjugates appear to be randomly distributed and to be consistent with a model in which disintegration occurs by at least two major, sequential, rate-limiting events. For conjugates containing one lymphocyte and multiple target cells, the mean rate at which a lethally hit target cell disintegrates is found to be independent of the total number of target cells in the conjugate. Our model predicts that in such multicellular conjugates, individual target cells lyse one by one, on average at approximately 30-min intervals, thus agreeing closely with previously reported experimental observations.