ADM1 represents a universally applicable biokinetic model for the mathematical description of anaerobic digestion of different types of organic substrates. Digestion of particulate composites is described as a five-stage process involving disintegration, hydrolysis, acidogenesis, acetogenesis and methanogenesis, of which the last three process steps are represented by growth kinetics of the specific degrading biomass. Decay of the produced biomass according to ADM1 is depicted by a recycle mass flux to the composite particulate substrate. Consequently two different actions are lumped into one process describing both conversion of feed substrate (depending primarily on influent characterisation) and generation of decay products (depending on digestion performance). In this presentation the introduction of a separate compound of inert decay products in analogy to ASM1 is suggested. Model calibration of separately monitored digestion of primary and secondary sludge (nitrogen content 0.030 g N/g TSS and 0.051 g N/g TSS, respectively) reveals the advantage of a clear distinction of disintegration and decay. The fate of nitrogen in the course of incorporation and release (0.016 g N/g TSS compared to 0.028 g N/g TSS) during digestion processes is comprehensible and the final ammonia concentration in the rejection water becomes predictable.