We have theoretically studied important dynamic processes involved in zero electron kinetic energy (ZEKE) spectroscopy using the density matrix method with the inverse Born-Oppenheimer approximation basis sets. In ZEKE spectroscopy, the ZEKE Rydberg states are populated by laser excitation (either a one- or two-photon process), which is followed by autoionizations and l-mixing due to a stray field. The discrimination field is then applied to ionize loosely bound electrons in the ZEKE states. This is followed by using the extraction field to extract electrons from the ZEKE levels which have a strength comparable to that of the extraction field. These extracted electrons are measured for the relative intensities of the ion states under investigation. The spectral positions are determined by the applied laser wavelength and modified by the extraction electric field. In this paper, all of these processes are conducted within the context of the density matrix method. The density matrix method can provide not only the dynamics of systems population and coherence (or phase) but also the rate constants of the processes involved in the ZEKE spectroscopy. Numerical examples are given to demonstrate the theoretical treatments.