The multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM) approach makes it possible to perform a check on the feasibility and desirability of patterns of metabolism of socioeconomic systems by providing a characterization at different levels and scales of: (a) the performance of socio-economic activities (for households, enterprises, economic sectors, national economies, world economy) and (b) ecological constraints (micro, meso, macro) by looking at the interference that the metabolism of matter and energy flows controlled by human activity induces on the expected pattern of metabolism of matter and energy flows associated with the self-organization of natural ecosystems. This paper presents three theoretical concepts behind the analytical approach MuSIASEM: (1) how to represent the endosomatic and exosomatic metabolism of societies using Georgescu-Roegen's flow fund scheme; (2) how to generate a Sudoku effect across representations of different units of production and consumption defined at different levels; and (3) how to perform an impredicative loop analysis when dealing with changes (evolution) of the characteristics of dynamic budgets of metabolized flows, represented across different scales. Since sustainability deals with "becoming systems"-systems becoming something else in their process of evolution-an analysis of sustainability must adopt analytical tools semantically open in their representation of change. MuSIASEM can do that since it is a "multi-purpose grammar", which can be used for building a shared perception and representation of this "becoming" when studying sustainability. That is, it entails an agreement on an expected set of relations between "relevant semantic categories" and "pertinent formal categories" across hierarchical levels and across different narratives: for this reason it represents a clear discontinuity from models developed within the paradigm of reductionism to deal with the issue of sustainability. (C) 2008 Elsevier Ltd. All rights reserved.