The IWA Anaerobic Digestion Model No.1 (ADM1) was presented in 2002 and is expected to represent the state-of-the-art model within this field in the future. Due to its complexity the implementation of the model is not a simple task and several computational aspects need to be considered, in particular if the ADM1 is to be included in dynamic simulations of plant-wide or even integrated systems. In this paper, the experiences gained from a Matlab/Simulink implementation of ADM1 into the extended COST/IWA Benchmark Simulation Model (BSM2) are presented. Aspects related to system stiffness, model interfacing with the ASM family, mass balances, acid-base equilibrium and algebraic solvers for pH and other troublesome state variables, numerical solvers and simulation time are discussed. The main conclusion is that if implemented properly, the ADM1 will also produce high-quality results in dynamic plant-wide simulations including noise, discrete sub-systems, etc. without imposing any major restrictions due to extensive computational efforts.