The in-situ observation of dendritic growth in lithium/polymer electrolyte-LiTFSI/lithium battery cells shows that dendrites grow up with about the same rate as anion migration. Memory effects have been evidenced in cycling experiments and limit the dendrites length. An overall movement of the electrolyte due to variations of electrolyte concentration in the vicinity of the electrodes has been observed too. (J.S.) 13 refs.