Using a method of laser ablation, a number of AgI-chalcogenide glass nanolayered films has been obtained with different thicknesses of the layers (10, 25, 50, and 100 nm). In order to study alpha a double dagger dagger beta phase transition in AgI, X-ray phase analysis has been carried out in the temperature range from 30 to 200A degrees C. A correlation between the layer thickness and the temperature of the alpha -> beta phase transition during the lowering of the temperature is found. An explanation of the correlation is proposed.