Even in fully-depleted (FD) SOI MOSFETs, the floating-body potential variations may lead to strong transient effects on the current characteristics. A physics-based model, enabling the fast computing of the potential variation with time, is proposed in this paper. The model is validated, for a wide range of technological parameters and biases, by 2D numerical simulations. This model reproduces the experimental data and clarifies the physics mechanisms responsible for the transient variations of gate and drain currents. Relevant applications in the field of EEPROM and capacitorless floating-body DRAM memories are addressed.