The application of single step or multiple anodic potential steps to highly concentrated solutions of N-vinyl-2-pyrrolidone leads to the formation of poly(N-vinyl-2-pyrrolidone) (or PVP) films on platinum electrodes. These films are insoluble in a good solvent of the commercial polymer. Multiple potential steps yield thicker films than a single potential step. Moreover, the PVP film thickness is maximum for a working potential amplitude of 1.7 V. Above this potential, the polymer film deteriorates by oxidation. In situ quartz crystal microbalance measurements show that the formation mechanism of polymer films cannot be attributed to an initiation in solution followed by precipitation of the polymer on the surface but rather to a gradual growth of the polymer on the electrode. This result is confirmed by the analysis of the electrochemical medium by different techniques which does not reveal the presence of polymeric chains in solution but only of dimer molecules. The molecular structure and the origin of these molecules are precisely established. From these results, we conclude that the polymer is chemically bonded to the platinum at the interface and grows progressively on the electrode surface. Both a radical and a cationic mechanism are examined to explain the above observations. A detailed theoretical analysis of plausible reaction intermediates suggests that only the cationic mechanism is able to account for all present experimental results and, in particular, for the occurence of a voltammetric current during the polymer growth.