Long-term aerobic digestion batch tests were performed on a sludge that contained mainly two fractions, a heterotrophic biomass X-H and its endogenous residues X-P, which were cultivated in conditions known to favor bio-storage (X-Sto). The objective was to model the stabilization of the sludge and determine the parameters of the endogenous decay processes, based on simultaneous measurements of the chemical oxygen demand (COD) and oxygen uptake rates (OUR). The respirograms were shown to have a two-phase structure that was describable with activated sludge model 3 (ASM3), but not with ASM1. Comparing the information from the COD and OUR data suggested the presence of two different groups of heterotrophs (X-Ha and X-Hb), one that decays with oxygen consumption and another without using O-2. A modified ASM3 model was proposed, which was able to fit the OUR and COD data from the digesters, as well as cases from the literature. (C) 2014 Elsevier Ltd. All rights reserved.