The features of 2D images based on the bispectrum invariant to similarity transformations (shift, rotation and scaling) are applied to the classification of color image data. The invariant features are calculated with the crossbispectra between color values, which retain information on spatial third-order correlations of color images. Three kinds of color systems (the RGB, L*a*b* and K-L like systems) are employed. Combining techniques of the distance values of the invariant features, including decision rules (average, product, minimum, maximum, median and distance of decision profiles) and voting methods (majority voting, Borda count and approval voting) are then compared. Computer experiment is done on the classification of 79 natural color texture images in the VisTex database suffering from similarity transformations by combining the cross-bispectral features. The results of computer experiment show that the classifycation performance is improved with the use of color values when the less correlated color systems (the L*a*b* and K-L like systems) than the RGB system are used. The average and maximum rules give the highest classifycation performance among the decision rules. Further, the Borda count is superior to the majority and approval voting.