Aerobic digestion batch tests were run on a sludge model that contained only two fractions, the heterotrophic biomass (X-H) and its endogenous residue (X-P). The objective was to describe the stabilization of the sludge and estimate the endogenous decay parameters. Modeling was performed with Aquasim, based on long-term data of volatile suspended solids and chemical oxygen demand (VSS, COD). Sensitivity analyses were carried out to determine the conditions for unique identifiability of the parameters. Importantly, it was found that the COD/VSS ratio of the endogenous residues (1.06) was significantly lower than for the active biomass fraction (1.48). The decay rate constant of the studied sludge (low b(H), 0.025 d (1)) was one-tenth that usually observed (0.2 d (1)), which has two main practical significances. Digestion time required is much more long; also the oxygen uptake rate might be < 1.5 mgO(2)/gTSS h (biosolids standards), without there being significant decline in the biomass. (C) 2014 Elsevier Ltd. All rights reserved.