The performance of the spectral classification methods is analyzed for the problem of hyperspectral remote sensing of soil and vegetation. The characteristic features of metric classifiers, parametric Bayesian classifiers and multiclass support vector machines are discussed. The results of classification of hyperspectral airborne images by using the specified above methods and comparative analysis are demonstrated. The advantages of the use of nonlinear classifiers are shown. It is also shown, the similarity of the results of some modifications of support vector machines and Bayesian classification.