The paper presents experimental investigation of the crystallization kinetics of thin (from several and up to 100 monolayers, NIL) amorphous ice films grown in a vacuum on clean and adsorbate modified Pt(111) and graphite (0001) surfaces. The crystallization kinetics was followed by the associated decrease of the desorption rate by isothermal desorption mass spectroscopy. The process is strongly substrate dependent for thin films (below 20-30 ML), gradually becoming substrate independent in 30-100 ML range, and approaching the bulk ice characteristics for thicker films. For thin films, the enthalpy of vaporization is 52 kJ/mol for the amorphous and 54 kJ/mol for the crystalline films. The activation energy for crystallization was estimated to be 75 kJ/mol. The crystallization is accompanied by an enhanced mobility in the film as demonstrated experimentally by following O-2 release during crystallization of ice films on O-2 precovered Pt(111).