This paper examines the performance of four classifiers for Brain Computer Interface (BCI) systems based on multichannel EEG recordings. The classifiers are designed to distinguish EEG patterns corresponding to performance of several mental tasks. The first one is the basic Bayesian classifier (BC) which exploits only interchannel covariance matrices corresponding to different mental tasks. The second classifier is also based on Bayesian approach but it takes into account EEG frequency structure by exploiting interchannel covariance matrices estimated separately for several frequency bands (Multiband Bayesian Classifier, MBBC). The third one is based on the method of Multiclass Common Spatial Patterns (MSCP) exploiting only interchannel covariance matrices as BC. The fourth one is based on the Common Tensor Discriminant Analysis (CTDA), which is a generalization of MCSP, taking EEG frequency structure into account. The MBBC and CTDA classifiers are shown to perform significantly better than the two other methods. Computational complexity of the four methods is estimated. It is shown that for all classifiers the increase in the classifying quality is always accompanied by a significant increase of computational complexity.