The galvanostatic oxidation of hafnium in different electrolytes was investigated by means of in-situ ellipsometry in the range 0-150 V corresponding to oxides thicknesses in the range 0-350 nm. The oxide surfaces were characterized by scanning electron microscopy (SEM) examination. Single and double-layer models were used to interpret the experimental results and it was observed that the nature of the electrolyte affects mainly the properties of the external thin layer close to the solution. The bulk oxide grown in H2SO4, NaOH and H3PO4, has a refractive index of 2.06-2.07 and an absorption coefficient of 0.02-0.03. The Delta-psi profiles recorded during the oxidation in HNO3 reveal different stages of oxide corrosion. The films formed in this electrolyte have the lowest refractive indices as a consequence of their porous nature. An electric field strength increase with thickness was observed which could be associated to changes from amorphous to crystalline oxide structure. This fact could produce internal stresses during the oxide growth resulting in an anodic fracture. The ellipsometric results of the present work confirm previous ac impedance investigations.