The novel approach to classification of spatio-temporal data based on Bayes discriminant functions is developed. We focus on the problem of supervised classifying of the spatiotemporal Gaussian random field (GRF) observation into one of two classes specified by different drift parameters, separable nonlinear covariance functions and nonstationary label field. The performance of proposed classification rule is validated by the values of local Bayes and empirical error rates realized by leave one out procedure. A simulation study for spatial covariance functions belonging to powered-exponential family and temporal covariance functions of AR(1) models is carried out. The influence of the values of spatial and temporal covariance parameters to error rates for several label field models are studied. The results showed that the proposed classification methodology can be applied successfully in practice with small error rates and can be a useful tool for discriminant analysis of spatio-temporal data.