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Collecting and updating forest inventory data play an important part in the forest management. The data can be obtained directly by using exact enough but low efficient ground based methods as well as from the remote sensing measurements. We present applications of airborne hyperspectral remote sensing for the retrieval of such important inventory parameters as the forest species and age composition. The hyperspectral images of the test region were obtained from the airplane equipped by the produced in Russia light-weight airborne video-spectrometer of visible and near infrared spectral range and high resolution photo-camera on the same gyro-stabilized platform. The quality of the thematic processing depends on many factors such as the atmospheric conditions, characteristics of measuring instruments, corrections and preprocessing methods, etc. An important role plays the construction of the classifier together with methods of the reduction of the feature space. The performance of different spectral classification methods is analyzed for the problem of hyperspectral remote sensing of soil and vegetation. For the reduction of the feature space we used the earlier proposed stable feature selection method. The results of the classification of hyperspectral airborne images by using the Multiclass Support Vector Machine method with Gaussian kernel and the parametric Bayesian classifier based on the Gaussian mixture model and their comparative analysis are demonstrated.