As ubiquitous conduits for intercellular transport and communication, gap junctional pores have been the subject of numerous investigations aimed at elucidating the molecular mechanisms underlying permeability and selectivity. Dye transfer studies provide a broadly useful means of detecting coupling and assessing these properties. However, given evidence for selective permeability of gap junctions and some anomalous correlations between junctional electrical conductance and dye permeability by passive diffusion, the need exists to give such studies a more quantitative basis. This article develops a detailed diffusion model describing experiments (reported separately) involving transport of fluorescent dye from a "donor" region to an "acceptor" region within a pair of Xenopus oocytes coupled by gap junctions. Analysis of transport within a single oocyte is used to determine the diffusion and binding characteristics of the cellular cytoplasm. Subsequent double-cell calculations then yield the intercellular junction permeability, which is translated into a single-channel permeability using concomitant measurements of intercellular conductance, and known single-channel conductances of gap junctions made up of specific connexins, to count channels. The preceding strategy, combined with use of a graded size series of Alexa dyes, permits a determination of absolute values of gap junctional permeability as a function of dye size and connexin type. Interpretation of the results in terms of pore theory suggests significant levels of dye-pore affinity consistent with the expected order of magnitude of typical (e.g., van der Waals) intermolecular attractions.