Two stochastic models on the growth of software errors under an imperfect debugging environment are discussed. The errors that are introduced into the software during the developmental phase are called primary errors, and these are assumed to be distributed according to a non-homogeneous Poisson process. Imperfect debugging of primary errors generates further errors, called secondary errors, into the system. These secondary errors are assumed to be generated according to a cluster point process. Two types of cluster point processes are considered, the Neyman-Scott and the Bartlett-Lewis cluster processes. The mean value functions for the number of primary and secondary errors are developed for both models and we use these to obtain some important reliability measures. We also develop a cost model and obtain its corresponding optimal release policies. Finally, we discuss parameter estimation based on the criterion of maximum likelihood and present a numerical example.