Composting is a complex bioprocess, requiring a lot of empirical experiments to optimize the process. A dynamical mathematical model for the biodegradation of the organic matter during the composting process has been developed. The initial organic matter expressed by chemical oxygen demand (COD) is decomposed into rapidly and slowly degraded compartments and an inert one. The biodegradable COD is hydrolysed and consumed by microorganisms and produces metabolic water and carbon dioxide. This model links a biochemical characterization of the organic matter by Van Soest fractionating with COD. The comparison of experimental and simulation results for carbon dioxide emission, dry matter and carbon content balance showed good correlation. The initial sizes of the biodegradable COD compartments are explained by the soluble, hemicellulose-like and lignin fraction. Their sizes influence the amplitude of the carbon dioxide emission peak. The initial biomass is a sensitive variable too, influencing the time at which the emission peak occurs.