We analyze the classes of problems with an objective necessity to use neural network technologies, i.e. representation and resolution problems in the neural network logical basis. Among these problems, image recognition takes an important place, in particular the classification of multi-dimensional data based on information about textural characteristics. These problems occur in aerospace and seismic monitoring, materials science, medicine and other. We reviewed different approaches for the texture description: statistical, structural, and spectral. We developed a neural network technology for resolving a practical problem of cloud image classification for satellite snapshots from the spectroradiometer MODIS. The cloud texture is described by the statistical characteristics of the GLCM (Gray Level Co- Occurrence Matrix) method. From the range of neural network models that might be applied for image classification, we chose the probabilistic neural network model (PNN) and developed an implementation which performs the classification of the main types and subtypes of clouds. Also, we chose experimentally the optimal architecture and parameters for the PNN model which is used for image classification.