Transcription factors have a major function in orchestration of gene expression programs which lead to the formation of new cell types and tissues in a developing organism. Their mode of action is not known; in particular it is not known whether they continuously bind to and dissociate from their target DNA or chromatin or whether, once bound they remain that way for hours or days. Clarification of this uncertainty connects closely with the stability of gene expression, a characteristic of the differentiated state of the cells, which for most cell types changes very little during life. The dwell time of transcription factors on DNA or chromatin which has been largely analysed by fluorescent recovery after photobleaching (FRAP) experiments do not measure the stability of gene expression. We have recently introduced a way of determining the duration of dwell time as well as the stability of the binding, in contrast to what was concluded by FRAP experiments. We found that in Xenopus oocytes, the gene expression can be stable for hours to days. We also have found that the formed complexes resist the competition by another template. It is suggested here that the binding of transcription factors may be stable and can promote cell differentiation at least for the non-dividing cell. In this article we aim to uncover the potential mechanism which may contribute to such stability of gene expression in nondividing cells.