This paper presents a theoretical investigation of the crystallization kinetics of thin adsorbed amorphous water films mainly based on our recently published experimental results [Lofgren et al., Langmuir 19 (2003) 265]. A nucleation simulation model, in which the time course of the growth of each crystalline grain is explicitly modelled, is presented and used to determine the location of the nucleation to be both in the bulk and at the substrate/water interface. The model also shows that a non-zeroth order of desorption from the bulk layer can be related to inhomogeneous adsorption. Further, a thermodynamic analysis of the experimental data is presented. At 145 K the critical size of a (bulk) ice nucleus is approximately 40 water molecules and the nucleation rate constant is 10(-6) s(-1).