In this article, an autonomous four-compartment model that describes the endogenous respiration in an aerobic biodegradation process is proposed and analyzed theoretically. First, the multi-time scale of the system's behavior, to be taken into account in subsequent analyses, is emphasized. Then, an identifiability and observability study, given measurements of MLVSS (mixed liquor volatile suspended solids) and respiration rate, is performed for use under practical circumstances, such as in state and parameter estimation. It appears that the process is observable, but not fully identifiable. Hence, for the identification of some of the model parameters, additional measurements or experiments, also indicated here, have to be performed. Furthermore, it is shown that, under quasi-steady state conditions which, in general, appear shortly after initialization of an endogenous respiration experiment, the model can be reduced significantly. Finally, results of parameter estimation from available data are presented and discussed.