Complex wastewater is defined in this context as containing significant levels of fats, proteins or particulates. High-rate anaerobic treatment of complex wastewater is becoming more popular due to economic and environmental advantages. However, treatment is complicated because of the high levels of solids and fats and lack of knowledge of degradation mechanisms. This paper is the first part of a study of a structural model describing degradation of complex wastewater. A structural anaerobic model is developed which extends previous research, of which the most recent described the anaerobic degradation of soluble protein (Ramsay, I.R., 1997. Modelling and Control of High-Rate Anaerobic Wastewater Treatment Systems. Ph.D. Thesis, Department of Chemical Engineering, The University of Queensland, Brisbane, Australia). This study incorporates hydrolysis of particulates and long chain fatty acid (LCFA) beta-oxidation. A set of physico-chemical equations describes gas transfer and ionic reactions and structured biochemical equations describe biological and enzymatic reactions. A generic parameter estimation methodology for application to full-scale systems is also proposed.