Photorefractive self-focusing and self-trapping has proved, over the past decade, to be an efficient low power method able to provide beam control and steering. Over the years, photorefractive SrxBa1 xNb2O6 has been shown to be the most promising photorefractive media in this field. Its ability to sustain photorefractive solitons at steady state has been thoroughly investigated. In this paper, the focus is set on the temporal development of self focusing in SrxBa1 xNb2O6, evidencing a soft transition from self-focusing through self-bending and finally optical-branching. This evolution is shown to occur not only as a function of experimental conditions such as electric field applied or beam intensity, but also as a function of time.