The mobility of GFP-tagged glucocorticoid receptor (GFP-GR) within the nucleus of cultured adenocarcinoma 3617 cells is being studied by fluorescence recovery after photobleaching (FRAP). GFP-GR is a protein transcription factor that is a ligand for mouse mammary tumor virus (MMTV) promoter sites within the nucleus DNA. To permit quantitative interpretation of the FRAP measurements, mathematical models were developed to describe the influence of intranucleus binding and diffusion of GFP-GR on the fluorescence recovery. The models include low-affinity non-specific binding to sites that are distributed throughout the nucleus, as well as high-affinity binding to a discrete array of promoter sites. The models take into account the finite volume of the nucleus. Finite element software is used to obtain numerical solutions of the governing equations in two spatial dimensions to accommodate the spatial localization of the high-affinity sites. The two-dimensional numerical solutions are validated by comparison to simulations from one-dimensional analytical solutions. Parameter sensitivity analysis indicates that ignoring diffusion can produce serious errors in binding parameter estimation. The models are being applied to FRAP measurements of GFP-GR with the high affinity binding region representing a localized array of repeated MMTV promoter target sites. One result was a sub-second estimate for the upper bound on the residence time of the transcription factor at the promoter site, which is surprising since transcription can persist on the time scale of hours. This finding raises questions about the role of rapid exchange in the mechanism and regulation of transcription. It suggests that the FRAP techniques being developed will lead to improved understanding of these complex intracellular processes. The analysis was refined to consider an eccentric location for the array and the proximity of the array to nucleoli.