Proper analysis of label distribution in metabolic pathway intermediates is critical for correct interpretation of experimental data and strategic experimental design. While, for example, C-13 nuclear magnetic resonance (NMR) spectroscopy is usually limited to the measurement of degrees of C-13 enrichment, more information about metabolic fluxes can be extracted from the fine structure of NMR spectra, or molecular weight distributions of isotopomers of metabolic intermediates (measured by gas chromatography-mass spectrometry). For this purpose, rigorous accounting for the contribution of all pathways to label distribution is required, especially contributions resulting from multiple turns of metabolic cycles, in this paper we present a mathematical model developed to analyze isotopomer distributions of tricarboxylic acid cycle (TCA) intermediates following the administration of C-13 (Or C-14) labeled substrates. The theory presented provides the basis to analyze C-13 NMR spectra and molecular weight distributions of metabolites, in a companion paper (Park et al., 1999), the theory is applied to the analysis of several cases of biological significance.